the impact of consumer behaviour on technological change ... · the impact of consumer behaviour on...

The Impact of Consumer Behaviour

on Technological Change

and the Market Structure

An Evolutionary Simulation Study

Dissertation

zur Erlangung des Grades Dr. rer. pol.

der Fakultat Wirtschaftswissenschaften

an der Technischen Universitat Dresden

Dipl.-Vw. Nicole-Barbara Buschle

9 April 2002

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&Z C =)*(P*)*H\[v X YX? C F C &T C E[aX)*I=)* C H]jE[_';NZ)*] C F E[_\ C F5)*FFI-G R7E C gE[hX)* HhF E)* ';E C .]H C ?h? C 5H RËT*)*H\[ Pa()*aE[5 C C HI-Z C .[![5EaX5NW=()gE[! C =()*Ph7E . C g[ |H'*][!H C C F©_dk+)X)* H C F FF .E C . N G C HI)E*F*7)EH\[HIE .-G .DNa j ;X?H\FEQ)**'.+ C ]FH)** E[Pa C P]'P *w C &X)* Hj5E[+*)* ADC w' )* 'P E[j ;X?HIEF_Ed-G C &(=)*(P *)*H\[X?)' C .FPh C FFTw'5E[! ;X?HIEF~)*F'HIE C C X)* H" C F'HF©ZN*)*H\[ |k[)*E[+E-G C &(%)*j[ &([)k .E[ Y&)E7E)\ C F5)*FQFI-G R7E C 5E[+X)* HjF E)* ';E C C F[ &([) ;X| C F .E')*=()lE[jX)*wF'HI g[jPaGFl5X)* H¨*)*H\[ H C ?¨F E C &(' *[Fk .E[ )**X?HIEE[+*(')*H|X)* H+F *X?)** C K=*'XX.NQ()FPh C F * F M Z[IE)*(&( C I . Nv&( C E w C dkF&(?E[X)* HgF E)* ';E C (*)*H\[hPaH\[5 C *Pa Z\7E Hg()%F;N C Pa HXX)*ZH\[ X 9FIH P vADC E[ C C D*w' C E R*)*H\[uPaGF P ACQSRT?H K @dn @VM . **'PaF~E[57E[aX)* H

p)*_F E)* ';EF HH()*F C &EH'PQ'R7E .-( F E)* ';E C =' C HIE C

FP (p)k[ H\[T C dk C E_E[!H C *'Pa)* X V H C *'Pa)[5EaFH F"[<k Ph C NX)* H[k *[E*=()Y|I=()*Q[Q\)E*)*H\[ C & A [Q*)*H[ C .N C Hv[ Y ;X|HIEFX)* H E_X5NWkj('F| X

E(p) =

∫ ∞

0

[1− FP (p)]dp.

A [hFH F]E©*)*H\[n > 1

E Pa [hk %(*)-(nX)* H

pj, j = 1, . . . , n VY

[Wk ¨';N =)*(P E[*)]k .E[ E[dkj_(*)-(FX)* HI%E[ ;X?HIEFX)* HW[k %X5N '!E[h ;X|HIEF -7'ajE[hPa C .PQ'P+E[

n(*)-ZF X)* H!=)*(P

E[W C dk C F E)* ';E CFP (p)

~Im :=

Pa C p1, . . . , pn ?hE[hPa C PQ'PgE[(*)-ZF©X)* H79E)

n*)*H\[ Yg[ C E[!F E)* ';E C E[]Pa C P]'PX)* H]79E)

n*)*H\[Y gF C F©

FM(m(n)) =X)*(

(m(n) ≤ p) = 1− [1− FP (p)]n,

] ! # vd ÌdmqIcq!qwVfla%ng`!b"c`D`!bVa k#_e"qwVflauIno_oaqDeV_Ìd e"k#u!a%cqwaSbVdmqDo`!d p d ì $ i qwbV_rVrVd e.cu!_Ve"n9'"bVdmq cd e/d p p $ta1`!bVaSu!a%no"ky`!d _ed egrVu!dmk#a1_ $o`|cd eVa%n $ihvxVuw`!bVauDqwa%cu|k|b~] [a^ qwpmd b`!p i nod / au!ae `Skc`!a%_u!d %c`!d _eg`!_*a#`!bVau /d `!b:qwa%$au|cpTu!a#vxau!ae"k#a%qDdmqDrVu!_ $dmnoa%ngd e U <57-@-*R 2

ce"n +1F8 d /UdF57- ;=>*>&XD'r~D>.#*Ay~] f ^9p `!bV_.b HI895VM -@+.:;=>*Y.#Ad p p "q`!u|c`!a%q bVdmq a10ort_ qwd `!d _e"q/d `!blVeVd vx_u!flp i7nodmq`!u!d $Vo`!a%n rVu!dmk#a%qbVdmqdmnoa%cq

cu!aSqwbV_#/egd egc aeVau|cpJzci~] #"sbVaSa10orta%ky`!a%n $cp Va1_v clu|ce"no_f $cu!dmc$Vp a

Pdmq9noa "eVa%ngcq

E(p) =∫∞

0[1 − FP (p)]dp −

∫ 0

−∞[1 −

FP (p)]dp' $Vo`1qwd e"k#a7rVu!dmk#a%q9cu!a7cp sc%ioq/r _ qwd `!d $a*'"`!bVa qwa%k#_e"ngd e`!a%u|cp $ceVdmqwbVa%q%'tqwaaa~("~ 11 -a#`1cp ~

;=>0O#XD'r~DY@G*Ay~

eZJ


C FE[" ;X?IHIEFTPa C P]'PX)* H!79E)n*)*H\[

E(m(n)) =

∫ ∞

0

[1− FM(m)]ndm.

g[u ;X|HIEF X)* H~ HI C *'Pa)Wk YX5NFH)**WE[~ C E C * . N!*)*H\[ n

C H)** %g[ ;X?HIEFW&Z C =)*(P C FF .E C ;*)*H\[ K= C E)*Pav)*F'HIE C ?E[X)* H M H C ? k)* .*E C

G(n) = E(m(n))− E(m(n+ 1)) =

∫ ∞

0

[1− FM(m)]nFM(m)dm.

g[ ;X?HIEF&Z C =)*(P C FF .E C 5E)*H[FH)**n C H)** ';g .g.k+NG

)*Ph C gX|(* .E .-Z A ¨ . **'PaF~E[57(;\ C C &h C =()*Ph7E . C C X)* HI YH(E.N ¬E[ C ¬k .E[~H C \ C *)*H[©H(E

cX?)Y(*)-77E C |E[]H C E'P_)YH\[G(*YE[]X;\ .Ph C 'PQ?)%(*)

-7E C n∗ *_E[57 .E7E 5gE["H C F .E C

G(n∗) ≥ c > G(n∗ + 1),

E[57Y n H\[(* C *hE[577

n∗ E[]H(% C FF .E C *)*H\[ c | *E[5 C ()w'5E E[" ;X|HIEF©? C Y7% C FF .E C ¬*)*H\[v g[)*I=()*

n∗ +E["*(';E C E E["H C *'Pa)* |X)*(P

Pa CE(m(n)) + c · n.

VY.E[('&([OwE &() PaGF| -Z)NaH)¨ C &( C )E G .j[5j*I-()E?kjaX|( C E J PS U ACR"X K @dn e M H)* .E H *aE[57hE[©H C *'Pa)* +FH * C )*'T C (X;E Pa .E[E[a**'PaX;E C PhFa7?d-Zl*w' C E R%*)*H\[ kj('FuPhaH C *'Pa)"?I*E)"t;?H'*!["H C FH F"EXwNEX .=')E[)g*)*H[ g? C 5H R A *w' C E R?*)*H\[h j**'PaFh C E[ %=)EPaIkj()* wE[(X;E Ph;X?( HINQ=()¨"H C *'Pa)[5E[])**)-7E C X)* H!X)*(X?)DN( Yg[)*Q YaH)\ C H)* .E HlX)* HI?E[])**)-77E CX)* H¨*~E[57a C N t;¬)Qk .E[¥©X)E .H|dkE[)**)-7E C X)* HWk j|HHX;EF C F C N t;¬) ?d-( .]k ¨?W)* HIEFv g[)**)-77E C X)* H

R)**'.E]=)*(P E[

HH'R7E C E[57E[ H("¨(;\ C C & C FF .E C X)* HI t;¬) c[5Ew'5E[

e(e


;X?HIEF? C gE[57gFF .E C 5X)* HYt;¬) %g[ C R jF C F+*(';E C E]E[

w'57E C

G(R) = ck .E[

G(R) =

∫ R

0

FP (p)dp.

V¥H C *'Pa)lk[Y[5[ .&([!*)*H\[QH(E[5[ &([)l)**)-77E C X)* H%E[5 C H C *'Pa)k[~[5Qdk*)*H\[ H(E ~g[W(X;E Ph*w' C E RjE)*H[ X?( HIN X !E~HHX;a Ct;¬)

p .p ≤ R

C F~E)* HI! . .p > R

Imt

?QE[ Pa C P]'P (*)-(F X)* H79E)

tX?)* wF . HIE.N C !X)* HI!X|)X?)* GF (*)-(Fv gg[ C |E[" ;X?HIEF~&Z C

=)*(P C FF .E C ¬*7)EH\[w'5

G(mt) =

∫ ∞

0

(mt − p)dFP (p) =

∫ mt

0

FP (p)dp

C F*)*H\[TE(X79E)gX?)* GFt .c > G(mt+1)

V *H C F¥H)* .E HW OwE &() P_GF+)*I=)* E~E[*'XX.N * F J PS ACR"X K @dn e Xv @ J( M HjE["PaGF(DX5)E R¬X5)E R w' . .)* 'PE[()N "?H'*"E["()* &( C E[jF Z;¬)* C X)* H C ;XR C Fv jF)EdkE[+H C H.'E . C E[57 .E[jX)* HD*I*E C &&( C E%)* C *X?H 5F (E[INQH CC ?+ C O ' C HF_ C X)* H+*I*E C &ZN!\[jH C *'Pa)* FH * C ADC [ *Pa C YX5X?) =-A F J1B5X K @dn @VM H(PaXR C W?(';E[uw' )* .'PbE[()NC g| C & EQ ;XR C *I-()Ev(*)-(FH C (Pa HYX[ C (Pa C Q C FWE[FI-((X C &5Fu¨F *w' )* .'P H C (Pa HH C H C E)E7E C &Ph C NT C F'EPa C "X)*GH**"EH(PaX?IE .E .-(Tw' )* ; g[)*I=()*E[©H C (Pa H©&( C E C [ .WPaGFY)*~EF'!EH[5 C &( C F X)* H!)*_*I] ;X H .E.NTwN~*)*" C EF jE[ )E* R C'HIE C ) ADC [ ¨PaGFI ZE[)*Y)*Ph C N_ F C E H)5)*Paj C FhPa C N H C *'Pa)* ADC H\[hX?)* GF G5)*PFIE)*Pa C %E[X)*GF'HIjX)* H VH C *'Pa)-G * .E C 5)*PX?)¨X?)* wFh C Fh .E[)';NGHH()*F C &YE"YFPh C FQ=' C HIE C C F ; .EE[+Ph)*I%()-ZE[+E()*+ .5E[X)* H! Y?d-Z![ )**)-7E C X)* H|)*I-G *[ )**)-77E C X)* H] C FTE)*H[ &Z C] _u `!bVa %! + g_v1qwa%cu|k|b r _p dmk#d a%q%'qwaa +.:92F572 M"d9R \ / ;=>*?&X0Ace"n 5 b b ]SR 2 ce"n U R -@-

;=>0O Yc.'rVr~FY.#Ay~"sbVaeF' g `!bVa nod / au!ae` ` "ce `!d `!d a%qDfld b`Iu!arVu!a%qwae `W` "cp d `Cig_uIqwd a7nod / au!ae"k#a%q%' cq9a~("~ 'V`|boalnod flae0

qwd _e"qs_v c7`!ap a%$dmqwd _erVdmky`!Vu!aCh ; C 5 R"] 1 2 ;=>0O0*'r~F#G@O&A(Ay~

eU


C E[ C GX?)* GFv %$ )*Pa+PhdNWH\[5)*&("F Z;¬)* C X)* H | C FT+5)*Pag C H'F C &QE[(*H')*)* C E.NW-G * .EFTH C F'E[!X)*GF'HIYX)* H C E[ C GYX?)* wFv +$ )*Pag C <k E[FPh C F~=' C HIE C C F~E[ )**)-7E C X)* H E[ H C *'Pa)*! C FuPh ; Pa !E[ )X)* EhH\[X?)* wF +Phw C &u'ETYE[ )a C dkF&(©?(';hH C E'P_)* ¨)**)-77E CX)* H .-( C E[u';N()* C F*)* +?I[5d-G (')hk .E[ C X|)* GF E[©E)E C * .E C?IDk+I C X|)* GFg gFIE)*Pa C FZN C F'\P_ C ?E[)**)-7E C X)* H C FE[C 'PQ?I) H C *'Pa)* D'H\ZN WH C *'Pa)*_-(WE[WPh)*(I D' C 'H\ZN C )*I-G *E[ )g)**)-7E C X)* H | C F C Ik3H C *'Pa)* C E)E["Ph7)EI g[TPh C )**'.aYE[X5X?)a E[57_E[X)* HF E)E .';\ . C - C *[ +';aE[)**'.E C &uPh7)EI_X)* HFw C _H C -()*&(E~E[H(PaX?IE .E .-(Ww' )* 'P X)* H ADC EF lE[_Ph)*I!X)* H_F'E! C C .EQE PaQEE[ ( C "X)* !Pa ; Pa C &X)* HI * %\[Pa C (X?(.N X)* H ADC E[ aPaGF jX)* HF *X?)** C W)* C .N H C * F)*F X[ C Pa C C GHH')*)* C &F')* C &E[hF'EPa C ]X)*GH*!ET C &7D)*' C w' .)E .'PH[57)\7HIE)* F~wN©h* C &(!X)* H g[IN~)* C )*H(& C FuY\Q(';EH(PaY%E[F*H)* ?F_Ph)*I%X)*GH* %g[ )**'.Fw C %H[5 C &(j=' C F5Pa C \.N" .| C E)NQ C Ik5)*Pa! "\ C C EH C * F)E7E C Wg[hw' )* 'PX)* HaFH)** ';Q .!E ?d-("E[ H(PaX?IE .E .-( Ph)*&( C ?H(X)* H VY.E[('&([ () X?)*[5Xa|H'* Y RPa C F Q=wH' kg Eu*[dkE[57 E[)*)*H C F .E C h' C F)Wk[ H\[ C H C (P]NFw C H C -()*&(~E H(PaX|IE .E .-ZTw' .G)* 'P C F~ C .NTHHX;EF X)* HQF *X|)** C C (';DRDw' .)* .'P X[ C (Pa C C [ X5X?)!E(&(IE[)]k .E[ OwE &() ! C *X )*F PQ'H\[ =')E[)Q)**)*H\[ C E[hE(X HaX)* HF *X?)** C W`% C DNu+PaX )* HI-G F C Hh*[dk!E[57"E[)*W7)E_F Z;¬)* C H! C X)* H=()![(Pa(&( C ('!&(GGF!)*Ph C C &d-()] C &E Pa_X?)* GF g[)*I=()*Pa(]+E[*'*w'5 C X5X?)*H C * F)*FQE)*I=';EjE[j)**'.E-Y RPa C FQ C FQFPa C E)E7EjE[57*a C _E[()*IE H=)EPaIkj()* C C DF&( C )E7E]X)* H!F E)* ';E C H C ?Qa\w' )* 'P(';EH(Pa V C E[)!H C H) C jE[_*'EIG' C Q .E)E7E')*]kg"E*'XXPa C QOwE &() "7*EPaX;E] ;XR C k[wN5)*Pa¨H\[5)*&(F Z;¬)* C jX)* H Y9E C H .EFWF;-(GH7Ej)*w=() C \ C H 9P/P ?HSLK @dn ( M FIRTJ C F P ACQSRTA P K @dn ( M C F ?ACBDQ1FIB K @dn nNM g[INPaX[5* FaE[57¨ C .N C Y RPa C F ¨**'PaX;E C [5E!?PaGF 5F_E]-(( Fa[ )**'.E[57 C .NW* C &(DX)* Hw' )* Q ; g[IN wFX57)*=)*(P3E[2DFF.N3 * PaXPaGF 7E[57 ?ACBDQ1FIB K @dn n <Xv Z^(J MH[57)\7HIE)* wN F C E H(H C *'Pa)* ' C .\)NFPh C F 7*w' C E Rw*)*H\[ ;F]*)*H\[

eZ^


H( C Fu F C E H5)*Pa a$')E[) \[N &()* E[57 D PaX|)=HI" C =()*Ph7E . C & 1 C *' <aH C lE*'XX?()X)* H%F *X?)** C K ?ACBDQ1FIB K @dn n Xv <Z^(J M%M dkjI-Z) 7E[INF Z;¬) C E[ )H\[( H"k[ H\[T C "E[]**'PaX;E C g=-A F J1B5X K @dn @VM PawF 5FE_(;\ C X)* H F *X?)** C C w' )* .'P XADC E[+PawF; FIRTJ C F P ACQSRTA P K @dn ( M H C *'Pa)*%)*jH[5)EHIE)* F ZN]' C .\)NFPh C FT C F[IE)*(&( C ('*)*H\[TH(E g[)*! g C &()*('XH C *'PaI)Egk .E[dk C F~ C E[)&()*('Xk .E[T[ &([T*)*H\[~H(E Y$5() ;F~*)*H\[~H( ¬aH C *'Pa)YH C?H(PaQX?)=HIE.N© C =()*PaF~?';!X)* H !g[_ F C E H/5)*Pa?[5-Z_ Pa C (XG( E H. NTH(PaX?IE .E .-(l C F X)* H_F Z;¬)* C H]Pa C &5)*Pa!)*_H'*F ZN~ C H)** C &Ph)*&( C |H(E C F gD*[5X?F-()E&(H(H')-( +ij*gF Z;¬)* C HgGHIH')g?H'*"F Z;¬)* C !(';EX';!I-("&( C )E7E C &F Z;¬)* C ]-()E&(_H(E ag[ )"Ph C \7EPa C ! E[57X?(* .E .-(j*)*H\[_H*E)**'. C w' . )* 'P3X)* H?d-Z¨\[jH(PaX?IE .E .-(¨X)* H ADCH C \)EE)=-A F J1B5X K @dn @VM FF .E C . NEYE[j C DX)* H¨w' )* .'P 7X?)*Ph C C X)* H"F *X|)** C PadN* GHH') C w' )* .'P V C DX)* H+w' )* .'P H[5)EH\I)E F_ZN X)* H¨-ZHIE() (E[ C 'PQ?I)%!5)*Pa C E[Ph)*( K=?H'*]=)*] C E)N **'PaF M C FTE[QX)*(X|()E C %*)*H[ C &WH C *'Pa)**hE[57 5)*PaPh ; Pa "X)* E ¬H\[ 5)*P [5I)*WX)* E v C FTH C *'Pa)**)*H\[© C C (X;E PhZkgN( g[w' )* .'P X)* Hg .E[)E[gH(PaX?IE .E .-(+X)* H K= .?*)*H\[aH*E)* )* ()E[+X)*(X?()E C |*)*H\[)* [ &([ M ()E[+)**)-77E C X)* H A ¬Y C DX)* Hw' )* 'PFGI C g ; E[)* + .E[)] kj7DX)* Hw' )* .'P() C _w' .)E .'P7W A "u kj7DX)* Hw' )* .'P ; E BT .a aF C F ZN E[TX)* HI-(HIE() 5)*PC 'PQ?I)! C FuX)*(X|()E C jdk+DX)* H5)*Pa *E[57"X)* E")* Ph ; Pa F ¬E[ )*7X)* H C F .E C [(.F C F© C .NH C *'Pa)*Yk .E[©<k3*)*H[~H(E?H(PaQ C =()*PaFv )*ZE[gPa C PQ'P X)* Hgw'5E[gH(PaX?IE .E .-(+X)* H C F E[gPh ; PQ'P X)* Hg E[Pa C P]'P .E[)|E[+Pa C (X?(.N"X)* H+()E[+X)* Hg7k[ H\[QE[+[ &([GDH(%H C *'Pa)*)*" C F Z;¬)* C |I kj C *)*H[ C &a C FX')*H\[5* C &a)E C F(Pa.N ?ACBDQ1FIB K @dn nNM FI-G R7E+=)*(PE[ D* PaX.gPaGF YZN**'Pa C & H C \ C R E H . N FPh C F =' C HIE C _ C EF¥ u' C .\)N FPh C F C F¥ PaXP_ C E C &~F Z;¬)* C H C \ C "Ph)*&( C H(E =()E[5)*Pa VYX5) =)*(PX)*d-G C &E[_ ; E C Ha+ C C y]C^ fl_u!aSu!a%k#ae`IcrVrVu!_ ck!bdmq 5V//d8]SR 2-ce"n + 1 L ;=>*>*?@A/bVau!a1`!bVau!a%qwVp `9_v C 5 R"] 1 2N;=>0O0#Admq

c#$_dmnoa%n $i d e`!u!_Vno"kydme lVe"k#auw`|cd e `i c$t_o`9noafhce"n ;ZqwaaSrVr~IG.@Ay~ R :95 R 2 ;=>0O ?.'r~0 X0G*A eV_`!a%q `!b"c` gqwjk#d ae `zk#_e"nod `!d _e"q vx_u`!bVaDa 0Vdmq`!ae"kya~~~!cu!a9u|c`!bVaunoap dmkc`!a

d `/`!Vu!e"q/_o`s`!b"c`9a10odmq`!ae"k#aSnoartae"nVq9k#u!d `!dmkcp p ij_e `!bVa p _ $"cp $tab"c$dm_us_vT`!bVac#$au|c&a1k#_ q`9k#Vu$a~ h

e(


F&( C )E7EuX)* H©F E)* ';E C *[~*[dkE[57WE[~X|)** \ C H C FF&()*~!X)* HF *X?)** C C [)PaGFI)*.NW C |E[E[!7=()*Pa C E C F**'PaX;E C g[)* +]H C E C ''Pl F C E H|';N()*+k[QPh ; Pa g\[Y ;X|HIEF';E DN_vE[ ) Pa EFk+.E[ v * ?E[IN©*)*H\[ C &E[Q ;X?HIEF C H)** C ';E .DN=)*(P CFF .E C ¬*)*H\[T gX|(* .E .-Z g[IN*)*H[*w' C \ .Nhk .E[)*Hv=()g_dk X)* H C Ph)*(Igk[ H\[ gH\[5)EHIE)* FwN C dk C F E)* ';E C X)* HI

FP (p)

ADC H C E)EE E[PaGFH .EFaX)*I-G ('*.NZE[H C *'Pa)*';N C HH()*F5 C Hkg .E[h CRE H"FPh C F=' C HIE C gg[] ;X?HIEF~&Z C =)*(P C FF .E C v*)*H\[~ C h C &()* PaX.N FIE)*Pa C F¥ZN E[F Z;¬)* C H?IDk+ C E[ ;X?HIEFPa C P]'P X)E .HE[H')*)* C W C F E[*'*w' C X|)* GFv HH(' C a=() E[;¬HIEaE[57_E[w'5 C E . NFPh C FF FX? C F C E[©X)* H© C FE[57hE[T-7'© *)*H[ C H)**hk .E[E[w'5 C E .DNaFPh C FF GE[YH C HX;7 C C F )*HIj';E .DNQ=' C HIE C ¨ PaXPa C EFv g[ C F )*HI+';E N =' C HIE C

V g!=' C HIE C lE[X)*GF'HX)* H

pGE[ &( .-( C X)* HY

E[) &(GGF p0 C F~E[ H C *'Pa)* vk+.E[

W A ! &( .-( C

V = V (p0, p) +W

VgW&( .-( C X)* HI C F C H(PaE[© C F )*HIh';\ . .DN =' C HIE C Pa*')*hE[©Ph ; PQ'P';E .DNE[57 H C ?_H\[ I-(Fv !g[ X)* HQF E)* ';E C Y&( .-( C wN

FP (p)k[)*

FP (·) jH C E C '('*.NaF Z;¬)* C E RYPa*¨I-Z)Nwk[)*! C FW[5+X?(* .E .-(YF C * .DNdFP (p)

CE["H(*F C E)-

[p, p]=()g*(Pa

p C F

p > p C

IR+ g[! ;X|HIEF©&Z C C ';E Na=)*(P *)*H\[ C &a C H"Pa()* gF C EFwN B

h(mt) =∫ mt

p[V (p0, p) +W − (n+ 1)c]dFP (p)

+∫ p

mt[V (p0,mt) +W − (n+ 1)c]dFP (p)

−[V (p0,mt) +W − n · c],

K JG @VM

k[ C ;FEPaX C &©H(aX?)_(*)-77E C c C F E[<kjaX)* HIE[ 5)*

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0=()

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' C H)\ C N¥ C H)** K= C E)*Paa\ k[57W GE C WE[T*)*H[)W[5aE H[5 C &(T .E? I=Y79E)Phw C &h C Ik (*)-7E CM g[ YH C E)EEYX)*(X?)DN©â C FTE[ C F C & gJ PS ACR"X K @dn 7U M E[57 C H)**F ' C HI)*\ C DN C E)*Pa!? I=?';E[ C .E R7¬F *X?)** C X)* H)*F'HE[" C E C * . NW*)*H\[v ACR"XI? C F gFIH P K @dn n %Xv j^7UZe M FF)**aE[Tw'E C 'D[dk P 'H\[ C =() Ph7E C ! C ('&([ hk[ H[ k+]F *H'**F C E[hH C E G g&ZF57EQ C F *H7*')*Q% C =()*Ph7E . C EhH C *'Pa)* Yg[IN©**'Pa]E[57 C WH C *'Pa)Y C dkYE[QX)* HF E)* ';E C *)-G C &~H C *'Pa) ?[5-G (')Q*'&(&(E E[57 )*&Z)*F*QE[X)* HF E)* ';E C E[)*Yk |?*(PaYH C *'Pa)*+k[_.k+NGj-G * .+Pa)EE[5 C C E()*|=()*gX')*H\[5* C & g[ )%)**'.E)*+* Pa )EE[(*g(;\ C F ZN FIRTJ C F P ACQSRTA PK @dn ( M 7 * dE[j[ &([)\[¨X)*(X?()E C C =()*PaF!H C *'Pa)* E[jdkj) lE[+-()E&(X)* H] C E[]Ph)*(d Y+[ F Z;¬)* C H C )**'.E )*]H'*F~wNF Z;¬)* C **'PaX;E C C H C *'Pa)* l C =()*Ph7E . C [ C E[_PaGF% FIRTJ C F P ACQSRTA P K @dn ( M C w' )* .'P7+E[H(PaX|IE .E .-ZX)* H j C .NaX?(** Y .]R)*&(X)*(X?()E C lH C *'Pa)*FG C [5d-(+X?(* .E .-(¨*)*H[ H(E J ACR"XI? C F gFIH P K @n nNM *[dk E[57 C E[ )jPawF¬!H(PaX?IE .E .-(X)* Hw' )* 'P Ï-Z C X?(** .l5H C *'Pa)*+[5-ZX?(* .E .-( *)*H[TH*E ¨g[ gF'"E E["HIgE[57E[)*])*".kgNG*(Pa"H C *'Pa)*k[*)*H[ Pa)E]E[5 C C H OG vE[ ) PaX .H7E . C Edk+)*F"&( *R<E . C YE[57 E[X)*<-G * C C =()*Ph<E . C EWH C *'Pa)*Ykg l C H)**!E[QH(PaX|IE .E .-Z C *%Ph)*IE C Fdkj)+E[!d-()E&("X)* H g[a|<-(DPa C E C F~X5X?)* H C | H7E&(()* Fu)*('&[.N© 5)*"&( C )E7E C . !g[';E[()* 7E[*X5X?)*_)*WH C -G C HF E[57 FI-G R7E C ]=)*(P E[ D* PaX]PaGF =()! C \ C Ha C E[a=()*Pg[IE)*(&( C (' &( C E )* C H*E)N ET(;\ C \C C DF&( C )E7E!F E)* ';E C X)* H C w' )* .'P %g[57Y 5F Z;¬)* C X)* H)**'.=)*(PE[" ; E C H!X?(* .E .-( *)*H\[TH(E .E[)H(PQ C Fk .E[ 5)*PagX)*GF'H C &a7F Z;¬)* C H(E()H C *'PaI)E[5-G C &_F Z;¬)* C )**)-7E C X)* H 9FIH P ADC \[WX5X|)* gE[) *H C F &( C )E7E C H C F .E C Q)* C .NG*F ' C F)k[57+\YX)* HIYF E)* ';E C Pa)*&(GI-Z C .v*'XX )*+ C FhH C *'Pa)* 5)*Y]X)* )E F C \ .H Qg[aPh C )*&('Pa C " E[57"I-Z C .¨H C *'Pa)* l=() C \ C H)*_X)* )E F C \ .H 7 ]X?(E[IN!k Z?j[IE)*(&( C ('%|H'*+E[j*)*H\[ X)*GH* EGH\[5E H

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P '[5d-(% F C E H( C F"X|(* .E .-Z*)*H\[!H(E ADC E[)H* <E[X)* HF \)* ';E C C C DF&( C )E7E J K @n Z^ M =')E[)]*[dk]E[57]H C H) C C &Tkj.)*hX)*(X|)E % C DX)* Hhw' .G)* 'P g`)*IE_|I*E)gE[5 C C w' )* .'Pk .E[F *X|)**FTX)* HI V3&( C )E 7E C H XI? P/P C F XWXK @dn (e M ZN A FIHI? K @dn(n M )*I-Z"E[57"E[a*'HH*QX?( H .E" C H)**gkj.)*gFX? C F C &Z7E .-(.NQ C E[X)*(X|()E C ¬' C C =()*PaF_H C *'Pa)* $5')E[) ;[Y*[<kjE[57j*(PaYX?( H .EQ C HI)E*YE[Pa(' C jl C =()*Ph<E C C Ph)*IPhdN[5-(©E[~(XX?(* .E©;¬HI Y * Ë[u-()E&(~X)* H©)* * ADC )*H C \'F;N TFIB.V?B C F E J1H/F/Q1F K J c(c(cNM &( .-ZI-G F C H =()+dkj)+*)*H\[H*E+E[57H'*YX)* HË] C H)** %g[INW)*&('E[57Ë[ PhdN ? C Y)** C =()E[YP - C I-G F C HWgE[h)*R7E C *[ X |I kj C C =()*Ph7E . C C F X)* H!=(' C F C E[h C E) C IPh)*(\ %¨N_ C E)*GF'H C &"H C *'Pa)* GX)*I=)* C H¨=() 5)*Pa F ?R VJ1B© C F FIBDQK @dn(n J M *[dk E[57Y C C H)**" C *)*H\[TH(EPhNW<kj)gX)* H ?HS 9PS FIB C F A FIBGK @dn(n J M GE C F_E[gPawF; H XI? P/P C F XWXLK @dn (e MEh_F;N C Pa H *I*E C &h C F*[<k E[57H C *'Pa)* |*)*H\[T?[5-G (')*_H C &( C )E7EFPh C FHINGH ADC H C E)EhE E[T\7E HPaGF H XI? P/P C F XWX K @n (e M E[IN~PaGF .9NE[_H C *'Pa)* *)*H\[ PaH[5 C *P EHH(' C "=()E[ F;N C Pa H Ë[PaGFw C E[=(dk C &gk+dN( V+E[¨?&( CC C &5H\[ X|)* GF (H C *'Pa)FH F[dkPh C NQX)* Hgw'\7E C [+k *[%E"[5-()*H .-(FaZNQE[g C Fa|E[gX?)* GFv g[ C w[H C .E[)+HHIX;+E[Y?+t;¬)j()¨H C E C 'YEPaX C & g[ j*)*H\[PaIE[wFWH(PQ C ;FGDEPaXD* ¨*)*H\[_ C F]*w' C \ ;*)*H\[ k[)*jE[¨H C *'Pa) EY(*)-(* P ' C ('*.N C C F(&( C ('*.NFIE)*Pa C F C 'P |)%X)* HY C H\[~X|)* GFv g[ Pa C Ë[57jH C *'Pa)*jPhdN_*)*H\[hk .E[WF x;¬)* C j*)*H\[ C E C * .E V H C *'Pa)jH C* FH F C aE (*)-(TX)* HW C FX?(EX? C [ a*)*H[ C F +H C *w' C E.N [ X')*H[5* hg[ "?[5-G (')"PhN~&( C )E7E_=';E')*_FPh C F ?w(Pa h$ )*Pa )*a E)*HIQE©E[*?G(Pa]ZN F'E C &TE[X)*wF'HI_X)* H uVY X)* HQH C ?WF Z;¬)* C H\[uX?)* wF ¬E[Q C .N-7'5] C =()*Ph7E . C =()YH C *'Pa)* YE[Q C =()*Ph7E . C ?(';X)* H(;\ C FT C E[!H')*)* C X?)* wFv C !)**'.YE[ X)*GH*Y gE[57E[" NGX Hw' )* 'PX)* H X57E[ gHINGH H

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ADC E[%PaGF E[)* lgH C E C ''P ; F C E H5)*Pal C F!H C *'Pa)* ADC H\[!X?)* GF 7C IkH([()%?H C *'Pa)*7+ C \+Pa*')*

µX|) 5)*P C E)*%E[gPh)*I V H C *'Pa)

H\[5)EHIE)* F wNQ C C RE HjFIPh C FQ=() C +' C . L%w'5.N [g C dkE[g*w' C Hv=';E')*X)* HF E)* ';E C %OG C HH C *'Pa)*jH C FRdNQE[ )¨H C *'PaX;E C Z=()¨H\[X?)* GF

t > 1=(dk

µt ≥ µ ~LH\[ H C *'Pa)Q[5]E©FH F?(';]E[ C 'PQ?)

ntYX)* HWw'\7E C Q[ C E C FQEu[5-()*H .-(F¥ZN E[ C F YX|)* GFt $()QH[

w'\7E C [W[5!E©X5N TH C \ C H(c TV H C *'Pa)]Pa C P_ ![ !E\H(E

K=*)*H[ H(E_X' X)* H M *' HI_Eu©E PahX)*I=)* C H)E7E1/δ

EuF *H(' C =';E')*O <kg]+';\ . .DN(

δ > 1Pa*')*"E[h PaX57E . C H EH C *'PaW C F "H\[(* C EE[57

©H C *'Pa)Q ] C F Z;¬)* C Q|I kj C X')*H\[5* C &©EGF5N 7 ©X)* Hδp()]E(Pa()*)*dk7

~X)* Hp V H C *'Pa) ';NG_ .

δp ≤ p C F .gE[X)* H Qdk+)]E[5 C ()Qw'5+E

[ )**)-7E C X)* Hp g[]R7*E) FIE)*Pa C FT C F(&( C ('*.NT C F©FX| C F C E[

H')*)* C Y C F C =';E')*"X)* H F E)* ';E C C F C E["*)*H[E)E7E&N( OG C H 5)*Pag)*"dkjFWE H\[5 C &(E[ X)*GF'HIX)* HgH\[X|)* GF GE[ C =()*Ph7E . C H C *'Pa)+[5+ C X?)* GF

tPhNa?(';EF57EFW C

t+1 g[)*I=()*5]H C *'Pa)+H C C .N

';N=)*(P 5)*P=)*(P k[ H\[T[![5)EIH .-ZF©aw'\7E C C E[!H')*)* C YX?)* GFv +$5()PaIE[GF((&( .HGH C -( C C HwE[+E Pa+[()* C

T %**'PaF_E"| C .E C F

T > 1 X

LH\[ 5)*P H[5)*&(Q .E](X;E Ph%X)* H%| C &~dk+)*WgE[WH')*)* C X)* HhF \)* ';E C C FWE[*)*H\[?[5-G (')+vE[H C *'Pa)* *

pt C FWE[*w' C H qnt ∞n=0

Gk[)*qntF C E E[X)*(57 .DNu=()Q~)E C F(P_.N *HIEF¥H C *'Pa)QE©(*)-Z

nX)* H

?HS 9PS FIB C F A FIB K @dn(n J XXv @ J(Je M F C F;N C Pa Ha*)*H\[ w' .)E .'P C F .Eg*X?HI 5H"DNGX?Yg=(.dk .-Z C E[E Pa[()* C

T Ft(p), πt, µt, qnt ∞n=0, ptTt=1

F C F;N C Pa H*)*H\[w' )* 'P .

@ 7jI-Z)NhX|)* GFt;&( .-( C

(µt, qnt ∞n=0, pt)wE[YX)* +l5)*P

πt ≥ 0 . .j*w

X)* H C E[_*'XX|()!Ft(p)

C Fu *E[5 C () w'5Eπt .E[ X)*GF'HI

X)* H g(';E* FE["*'XX?() W C FJG 7I-()NX?)* GF

t(qnt ∞n=0, pt)

)*X)** C EE[uX;\ .PhY*)*H\[ |[5d-G (')H C *'Pa)*&( .-( C E["H')*)* C C FE[ =';E')*"*w' C H!X)* H F E)* ';E C

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V \7E C )NYw' )* .'P .F C F]l+F;N C Pa H*)*H\[!w' )* 'P C k[ H\[Ft1(p) =

Ft2(p)=()I-()N

t1, t2 ≤ T gV C C D\7E C )NF;N C Pa H!*)*H\[©w' )* 'P=()k[ H\[

E[)*! C C E&()z|*_E[57=()I-()N

t ≤ T − zFt(p) = Ft+z(p)

5 HF_HINGH .Hw' )* 'P ~VgHIE .-(FPh C F 7 X?)* wF

tADt

% QE F E~?WX?(* .E .-(W .©X?(* .E .-(Pa*')*!%';N()*EPaX!7Y C !X)* H

ADt = 0 .E[)*! C h*)*H\[~HIE .-G .DN

C X?I)E .GFt C F ;E[)*I=()* C _X')*H\[5*" +X|(** %V F;N C Pa H*)*H\[w' )* .'P

H[57)\7HIE)* F~ZNT C F(&( C ('?G(Pa .E[)*Q)*]X?)* GFY7Yk[ H\[~HIE .-(]FPh C F© )*h C FE[)gX?)* GF7gk[ H[T7HIE .-Z FPh C F g&()*7E)+E[57

µ

ADC ?HS 9PS FIB C F A FIB K @dn(n J M 7E[+)**'.E H XI? P/P C F XWX K @dn (e M )*(;\ C F*X?H RH* A vH C *'Pa)*EPaX C .NW C H5H[*)+k ¬H\[5)*&(E[]Pa C (X|(.NX)* H

p∗ A E[!X)*(X?()E C H C *'Pa)*k[W(*)-(QPa()* E[5 C C

X)* Ha "X|(* .E .-ZF *X?)**F X)* H_w' )* 'P k .% ; W$ C N l .+%H C *'Pa)*(*)-Z+Pa()*¨E[5 C C jX)E .HE[+w' )* .'P3X)* H¨k ww'5GE[+Ph)*&( C wH(%X)* HI g[w' )* .'P X)* HgF E)* ';E C %FIE)*Pa C F wN]E[w'5 DX)* %H C F .E C &( .-Z Cq C FE[ Pa C (X?.NX)* H

p∗ g[ H C F .E C PaX. .WE[57 C w' )* .'P,[ &([G

X)* H5)*PaQ*j=Ikj) &(GGF]E[5 C dk+DX)* H 5)*Pa g[(X;E Ph¨*)*H\[¥E)E7E&N H C *'Pa)]FX? C FQ C E[h ;X|HIEF &Z C =)*(P *)*H\[

G(·) C E[a'*'5k+dN E C w' )* .'P %E[ ;X?HIEF &( C =)*(P# C FF .E C +*)*H\[w'5a .E_H(E VYH C *'Pa)**)*H\[=()g7Pa(gDkjaX)* HX|)X?)* GF ;E["H C F .E C g* PaX.N

G(p∗, q) = c.K JG KJ M

.-Z C E[!)**)-7E C X)* Hp∗¬a' C w'

c∗ > 0 ; EE[57YE7E 5H C F .E C K JG KJ M

A *)*H[~H(E ;HFc∗?E[)*Q Y C .N C ]* C &(DX)* H!w' )* .'P ; EYk[)*_

5)*PaH\[5)*&("E[!)**)-77E C X)* H +$5()c = c∗

?_' C w'!X)* HDF *X|)**F©w' .)E .'P ; E Z C F] .

c < c∗7E[)*+)*Dk+YF *X|)*EIF X)* H¨w' )* 7\j C FQ C ' C \

C g[a)**)-7E C X)* H_FX| C F] C =';E')*_X)* H_F E)* ';E C C F lE[w' lk C !)*Ph C H C \ C Yd-Z)E["H(')**]E Pa g[] C F(&( C ('*.N-7)NG C &a)EIEI)*-77E C X)* H C O ' C HjE[ ;X?HIEF&Z C =)*(P*)*H\[ C FaE[E)*H[W C E C * . N ADC E[ k+N GE[)*)*X?)* wF HgPad-ZIPa C E_E[57a&( C )E7ETHNGH HX)* HDF *X|)**Fw' )* ©=() E[\W C F ' C \hH* Tg[WIN Pa C ]gE[ !F;N C Pa HaPawF¨ "E[hX?(** .N-)NG C &h)**)-77E C X)* H g[]HINGH Hl?[5-G (')Y C F'HF©ZNE[](*(*H C HQ C =()*Ph7E . C |E[QE Pa]X)*I=)* C H_¨H C *'Pa)*3K D PaX57E . C H M v C F©E[ )X|(** .DN

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+X?(EX? C C &X')*H\[5* C &T .g=';E')*aX)* HaF E)* ';E C "Pa()*aF;- C \&(('"E[5 CE[aH')*)* C ?HS 9PS FIB C F A F1B K @dn(n J M FPa C E)E7E_E[_\ *[Pa C !HINGH H;X)* HDF *X?)**F_w' )* =()E[g\g C F_' C \+H*ZN C 'Pa)* H; wPaX( C F C .NG*Ë[+X)*(X?I)*E I5E[jX)* H+ C F FPh C F HINGH VF EF;- C \&(jE[ DNGX?F;N C Pa HPawF| %E[57Ë[Y&( C E+)***'PaFhE![5d-(X?)=HIj=()** &([Z * E[IN C dk E["H')*)* C F E)* ';E C gkj?=';\')* X)* H"F E)* ';E C 9FIH P VY!E[a PaX5HI"+E[aPh C **'PaX;E C ] C F E[aF)* .-G C &=()*H!gX)* HF *X?)** C ?HPaHHX;\.N HI) ¨ C Ik)**)*H\[ C E)*_Pa)*&(Fv L%PaX )* H(*)-7E C "|HPa E[ =GH'"+7*E C \ . C *E[57 E[a**'PaX;E C "Ë[_PawF[5d-(g| C F'EF EE[+*X?H 5Hg PaXË[57%' C F)* %E'F;N( S (¨XX H7E . C )*I=)gE E[" C F'E)* Rv()*&Z C <\ . C .E)E7E')* ADC E[F;N C Pa HW*7)EH\[ PaGFj A FIB C F gJ K @dnn ^ M E[\)E C &©X?( C E[W(*)-77E C E[57Q C Ph C N H C (Pa Ha*HIE()*]E[)*)* C C DF&( C )E7E 5)*P D* F E)* ';E C C F 5)*PaY) C X|(* .E .-Z!X)* E Y$5')E[)*Pa()*?R)*&(5)*Pa'*'5.N) C[ &([)¨X)* EE[5 C *Ph)5)*Pa A FIB~ C F J K @dn(n ^ M ;XR C E[* C F C &(jZNX?(* .E .-(¨H C *'Pa)* *)*H[QH(E (k[ H\[ )*j C E)*X)*IEF %Pa*')*jIK= P M Pa . DN C Ph)*(I a$5')E[) lE[IN )*&(' E[57! C E) D C F'E)N©F Z;¬)* C H] C E[_H()*)*R7E C?IDk+I C X)* E% C FQPh)*(I*[5)*%H C |+ ;XR C F ZN]H C *'Pa)* (*)*H\[_|[5-G (') A FIB C F J K @dn(n ^ M **'Pa_H C *'Pa)*] C F 5)*Pa E?_ F C E H g[aH C *'Pa)*![5-(hFdk C kg)*F *(X C &FPh C F H')-( .-( C C .E.N C E C FuEX')*H\[5*H\[WX?)* wF ; C Fh C dk E[X)* HF E)* ';E C Qd-(( F_E[57jH C *'Pa)*jPhN_|H(PaK C )*.N M X?)=HIE.N~ C =()*PaF |(';]X)* H ." !**'PaF E[57 E[IN )*a C NuE~)*PaPQ?)]E[WX)* H7E[*)!=)*(P k[(P E[IN ?('&([ZQE[X)*I-G ('QX?)* GFv *)-G C &E[hX)* H_+E[ "*)" "=)*agH\[5)*&(a C E[ C GQX?)* GFv ADC ()*F)"E(;\ C ©X)* HY C E[) *) ¨©H C *'Pa)_[5QE~X5dN ©H C \ C _*)*H\[¥H(

c

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δ > 0 g[ 5)*Pa][5-(hE[a\7Pa

H C \ C WPh)*&( C +H(Ek ADC H C E)EhE E[TX)*I-G ('*.N¥Pa C E C FPaGF jE[

H(E-7)N_d-()%E[H(')**?E Pa+F'E" ;(&( C ('¨*[wHw wk[ H\[h)* C FX| C F C E.N C FT F C E H NWF E)* ';EFTH)*(*E[5)*Pa B C .NWDkjh\7EH(E)*!dkjF [ &([H(E

kH C F<k H(E

kL < kH $5()g C C F .-G F'57+5)*P Ph)*&( C ?H(E)*! C

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';EGH()*)*R7EFh)E C F(P-)* Rktk .E[!E)E C * .E C X)*(5 DN

1− β=()k[ H[W .j

**'PaFE[57

`(kt = kL|kt−1 = kL) =

`(kt = kH |kt−1 = kH) = β >

1

2

C F

`(kt = kL|kt−1 = kH) =

`(kt = kH |kt−1 = kL) = 1− β <

1

2.

.E[X)*(5 DNβ5)*P)*Ph C j C E[H(\7ElE[X)*I-G ('gX|)* GF C FWk .E[

X)*(5 N1 − β

E[WH(_\7EWH[5 C & `%)* HI H C ?F'EF k .E[(';]=')E[)H(E G';j 5)*P[5%E!Xh C Pa C FQE[57¨ZN C H)** C & E[X)*GF'HI¨X)* H .k (*X57E)* C C &hH'E(Pa)* "g[INTk C )*IE') C .%E[QX)* H] FH)**Fu?H'* E[IN)*gwHFGD C 7 C E[) 5)*P% C & E[ 5)*PFG C C H)**+E[gX)*GF'H¨X)* HI g["E)E C * .E C X)*(5 DNW C O ' C HY*_E[")*IE') C =)*(P*)*H\[© .H C *'Pa)*';N)*X?7EF.N 5 * ;E[")*IE') C =)*(P *)*H\[T C H)**!

β C H)**

V C w' )* .'P jH[5)EHIE)* IFwNW]X)* HYF E)* ';E CF (p)

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FPM k .E[

p ≥ 0

g[j(X;E Ph(E)E7E&N"|H C *'Pa) l PaX .H E N & .-Z C ZN E[¨=(.dk C &X)*(X|(* .E C !x<2-%2?6=4<692?>o / (+*,)!$#Y2& !$a&! 7' W*, #Y !Y*, 2& ! # ! &8 ! &,'#% H

p ≤ ϕ W*,

ϕ !Y*, &!$#%#% ;# #Y2H1 #% #Y!% ' 8J1 &

ϕ = b+ (λ0 − λ1)

∫ ϕ

p

FP (x+)

ζ + λ1FP (x+)dx

K JG e M

= b+ (κ0 − κ1)

∫ ϕ

p

FP (x+)

1 + κ1FP (x+)dx

K JG U M

J#Y!Y*κ0 = λ0/ζ

&κ1 = λ1/ζ

(+*,!$#Y2& !$a&! 7'3. &O&8 !$6&= ! 2 # -! &8 ! &,'#%H 3 !$#% !$ ' X !Y*6&!Y*,= ,! 1

"sbVa%qwaSfhc%icpmqw_ $ anodmq!k#_Ve `!a%n9'&$Vo`/d `!bV_o`Dp _ q!qs_v aeVau|cp d `Cih`!bVa7nodmq!k#_Ve `9u|c`!a1dmqDqwa#`9aa` "cpN`!_au!_"~ # Ìcpmqw_lfhci $taa%k#_eV_fldmk1rVu!a%q!qwVu!a1d e"q`!a%cn_v /d p p d e.eVa%q!q~ _u9p _# d e"k#_flabV_"qwabV_pmnVqz`!bVdmq9fhci

p a%cn `!_h`!bVa Id / ae a1/ a%ky`9`!b"c`/`!bVa7noafhce"ngd e"k#u!a%cqwa%qsd v`!bVaSrVu!dmk#aSdmq9d e"k#u!a%cqwa%nN~izoÌd / ae__VnVq/cu!aeV_`/`!bVaqw&$ %Ca%ky`9_v `!bVdmq9q`!"noi~! aa 1 2989+ ]5bD/sa#`scp ~I; . . ..'r~0 .*>@AB' 1 :&89+.2 /%+.2 ce"n ),+ \8]SR 2F2 ;=>*?*?.'r~0&X*X0AB' ce"n K*R 2 F+.2

+.:JM-ce"n + 5 +.: ;=>*>*?.'r~F*?0O&Ay~!y] >bVa#`!bVau1ce aa` "cp rVu!dmk#a_/ au z_Vpmn $ta ckk#aro`!a%n noartae"nVqI_e `!bVaìrta _v `!bVa,__onN~ b"ce.d e.

`!bVaSqwVrVrVp d au/_vc q`|ce"nVcu|nod a%n __Vnh"qw"cp p iE/d p pNeV_`9kc"qwaIf7"k|b `!u!_&$Vp a%q%'0/bVaed `/dmq/cq!qwVfla%nh`!b"c``!bVak#_e"qwVflau|qsno_heV_`/b"c#$a1rVu!a#vxau!ae"k#aqzvx_u9clk#auw`|cd egqwVrVrVp d au9_us_`!bVau9q(/d `|k|bVd e.hk#_ q`|q~

^(


OG C HL%w'57E C K JG e M C H.'FjX)* Ht;¬)¨F E)* ';E C %k .E[hPh*¨X?( C E G .¨[5¨E]?'*F

FP (x+) := limε↑0FP (x + ε)

C EFTFP (x)

B©g[Q-()E&(]X)* H!t;¬)EFP

[p] +**'PaFhEQ? C .E VYg]H C *w' C H ;E[Y)**)-7E C X)* Hϕ C .E¨kj¬

p *'XT *'XX9K

FPM

$ )*Pa F C !t;¬)]X)* Hp > ϕ

|H'*hE[)k *E[IN~kj('F C !* C NwE[ C & C Fkj('F C X5)E H X57E C E[ Ph)*(I C NPa()* %g[w'

p ≤ ϕ

<=:0:%< DRTGK DG DR > BHECACEHI6E/B @;FHS"B R+I AC@ S

ADC E[ !PaGF lE[)*W)*aDkj©X)* HhF E)* ';E C =' C HIE C !k[ H\[ [5-(hET|hH)*.NF E C &(' *[F C Pa.N

FP (p) = Prob(P ≤ p) C F

GP (p) = Prob(P ≤ p) FP (p) E[QHI'P 'R7E .-(!F C * .DNTX)* HYt;¬)*F~ZNE[ HIE .-(5)*Pa v*hHFE[QX)* H

t;¬)]F E)* ';E C C E[hH C E)E)N GP (p)

!E[hH'PQ'R7E .-(_F C * . N +E[hX)* HHIE'5.NYX5 F wNH C *'Pa)* E I\[E%X)* H7kg[ H[ E)EF$lXRH C E[%Ph)*(I g[)*I=()*

supp[GP ] ⊆ supp[FP ] !g[ C

GP (p) = 1 − GP (p)H C | C E)*X)*IEF

E[=)EHIE C H C *'Pa)*ak[ X5N¥ X)* H$* H\ N [ &([)_E[5 Cp C E[EGH\

HIE'5H'E(Pa)* A ] . WH C * F)*FE[57YH C *'Pa)*';N7 X)* H~E)* HIE.N[ &([)WE[5 C

pE[

=(dk C & H C *'Pa)%Pad-ZPa C E%H C | F C E 5F_ C C NQ C E)-[t, t+dt]

C EF;N\7E"FPa(&()EX[ Hw' )* 'P V] `E C E R%H C *'Pa)*])*_k C &WE©HHX;Q C N

P > p .p ≤ ϕ

OG lE[ O <k=)*(P X?E C E RvH C *'Pa)*-K

UM EaHIE'5vH'E(Pa)*-K

EM

λ0 · F (p) · U · dt,k[)*

F (ϕ+) = 0

Y g .E[uE[aH C \ C ])E7Eλ1 ;X?)* C HF H C *'Pa)*])*h E PaX)*d-ZQE[ )

* .E'57E C % E E, C F 5)*P E[57_t;¬)*a~X)* HWk[ H[ E)* HIE.N dkj)QE[5 CE[!X)* H"E[IN[5-(]X5 F*a) jg[ O dk3%H'E(Pa)*Pad-G C &_=)*(P E[ )(F*'XX )+Ea C E[)w'5

λ1 · F (p) · E · G(p) · dt.!#aa 1 2989+ ]5bD/Ia#`Dcp ~F; . . ..'r~D.#.@Ay~

^


iY g[ O dk D' C 'H\ZN "H C *'Pa)* | * ;E[(* k[aPa<-(=)*(PH C *'PaX;E C KEM

5H\hEQE['D' C E7E 5F \7E3KUM |H'* E[ 5)*P7+k[ H\[E[IN|('&([ZgE[

X)*GF'HIE["X)*I-G ('X|)* GF[5&( C "5 C w)*'X; 5 g&( .-( C ZN

ζ · E · G(p) · dt.

ADC $ &(')*"JG @ 5¬E[ F*H)* ?FH C *'Pa)Pad-ZPa C E)* *'PaPh)* F ;k[)* E[I*E)* C HI )*H)*I=)gE E["*X|H 5F O dk

- L

6 6

µ´¶³

µ´¶³

V

i µ´¶³

$ &(')*!Jw @ jij C *'Pa) S d-(Pa C E

ADC w' )* 'P E[ O dk C C Fa(';?\[EwHQvHIE'55H'E(Pa)*%k[!X5N_"X)* HE)* HIE.N?d-(

pPQ'?" F C E H %L%w'5 C &QV3k .E[E["*'P 7% C F©i&( .-(

λ0 · U · FP (p) = ζ · E · GP (p) + λ1 · FP (p) · E · GP (p), or

λ0 · U · FP (p) = (N − U) · GP (p) · [ζ + λ1FP (p)]

K JG K^ M

.p ≤ ϕ

| C F O <k)* )*_ .p > ϕ

$5()

p = p .!

FP (p) = GP (p) = 0 C F

FP (p) = GP (p) = 1 C F L%w'57E C K JG K^ M

PaX .jE[57

λ0 · U = ζ(N − U)() U

N=

ζ

λ0 + ζ=

1

1 + κ0

K JG M

k[)*κ0 =

λ0

ζ

^ n


a*'P'X E[ =(dk C & X)*(X?(* .E C H C ?"Ph C \ C Fv B

!x<2-%2?6=4<692?>o o &3 ! & ' ! &! 8 2 7a& ,*"#% "#Y # #Y"2 1 23 !J*6& !Y*6&!

U

N=

1

1 + κ0

& K JG K M

GP (p) =1− FP (p)

1 + κ1 · FP (p),

K JG M

J#Y!Y*κ0 =

λ0

ζ

&κ1 =

λ1

ζ

L%w'57E C K JG K M H C 5)*Pa\[5<E[]X)*(X|()E C D' C 'H\ZN !H C *'Pa)*Y C H)**k .E[E[5 C w)*'X;EHIN )E7E

ζ C F FH)** k .E[ E[*)*H\[ ;¬()

λ0 L%w'5<\ . C K JG K M

(;\ C FZNw'5 C &]E[ O dk C E_ C F(';7U

L%w'57E C K JG M &( .-Z¨E[YE)*'HIE')E¬)*R7E C *[ Xa?IDkj C E[YF E)* ';E C HIE'5.NX5 F©X)* H

GP (p) C F©E[QX)* HQt;¬)F E)* ';E C

FP (p)k[ H\[u Y PaX?(*F©ZNTE[

EF;NZD\7E!FPa(&()EX[ Hw' )* 'P ; *&

FP (p)= 0 ⇒ GP (p)= 0,

FP (p)= 1 ⇒ GP (p)= 1,

FP (p)=12⇒ GP (p)=

1+κ1

2+κ1.

g[ _Pa C E[57a .E[X)* Ht;¬)_F E)* ';E CFP (p)

_&( .-( C j C w' )* .'P E[F E)* ';E C

GP (p)lHIE'5.NQX5 FaX)E .HjH C ?FIE)*Pa C F G&( .-( C E[57E[YX5)EP

IE)*κ0, κ1

()λ0, λ1, ζ

)* ;(&( C (' $5()κ1 > 0

C F X)* Hp .".k+dNG [(F

E[57FP (p) ≤ GP (p)

v * vE[()NT PaX?(* v[ &([GDX)* H5)*Pa )*QF)* .-( C ('; E[Ph)*(d !#aa 1 2989+ ]5bD/Ia#`Dcp ~F; . . ..'r~D.#.@Ay~! DeVahk#_Vpmn-cpmqw_d fhc&d eVal`!b"c`7qwa%cu|k!b:d e `!ae"qwd `!d a%qnoartae"n9'Tvx_uSd e"q`|ce"k#a*'T_e)`|boaju|c`!d __v "u!fhq1`!_

k#_e"qwVflau|q%'Vcqsqw.*a%q`!a%n $i 1 2989+ ]5bD/Ia#`Dcp ~F; . . ..'r~D.*#Ay~

c


<=:0: RTQHG ?=EC@JI @ R1DR+I6@ ;RTFHRT@;BHS E I S

$5)*(P E[_X)* H t;¬) F E)* ';E CFP (p)

.=(dkYE[57!H C *'Pa)")*H -Z!X)* Ht;¬)?d-Z

pk .E[]X)*(5 DN

FP (p) = Prob(P > p) g[+X)*(P35[dk H C *'Pa)*

C F 5)*PaH C |gPh7EH\[F C E[gPh)*I% *(.-ZF ZN]E[g**'PaX;E C E[57%H C *'Pa)*F)Edk X)* HTt;¬)*hwN¥)E C F(Pa.N X H\w C & 5)*Pa +k[)*~H C *'Pa)*W'*~ ' C .=()*PEPaX C & *H\[Pa I F C E"E[!Pa*')*!HIE .-(5)*Pa +V 5)*P HFTHIE .-(! . . .Y EaEI7!] C _' C .!+ .E"X)*GF'HI A ] "HF),! ,!$#$&Y '~HIE .-Z_ .j .!t;¬)*!&(GwF]7WX)* H]E[57FG C ;HIFu\[Q)**)-77E C X)* HIQE[QH C *'Pa)* *

p ≤ ϕv()

p ∈ supp[FP (p)] uVY.E[('&([ 5)*P PhN [5-ZhE[X?(** DN H)*)NG C &©('; X)* H

F *H)* Pa C 7* C Pa C &u .E_H'E(Pa)* j ._ a**'PaF E[57aH\[ 5)*P t;¬)*a C .N C X)* HWEu¨ .EQH'E(Pa)* V 5)*Pa C E C F Eu ;X5 C F wN C H)** C &©E[ )]Ph)*(I*[5)*

Z · FP (p) QE[Pa*')* 5)*Pa t;¬)* C & ~X)* H?d-(

p g[IN H C ?

)*R7EFEE · GP (p)

5k[ H\[T gE[!Pa*')*!H C *'Pa)*X5dNG C &h_X)* H!?d-Zp A

=(dkjE[57E["EF;NZD\7E C 'PQ?)gH'E(Pa)*X?) 5)*PX5NG C &p #

l(p) =E

Z· d GP (p)

d FP (p)=

E

Z· 1 + κ1[1 + κ1FP (p)][1 + κ1FP (p+)]

,K JG nNM

k[)*dGP (p)

C FdFP (p)

)* E["F C * .E gGP (p)

C FFP (p)

.-Z C E[jPaGFGX5)EPaIE)* 7E[ C =()5)*P t;¬)* C &YYX)* H

pl(p)

&( .-(E[ C 'PQ?)H'E(Pa)*Q(';Q

EE[ 5)*P H C ;X?HI C E[hH')*)* C X|)* GFv TV 5)*P t;¬)* C &

p = pH C ;X?HI

l(p) = EZ

11+κ1

H'E(Pa)* K=* C HF (p+) = F (p) = 1

M Gk[)*5)*Pt;¬)* C &

p = pH C ;X?HI

l(p) = EZ(1 + κ1)

H'E(Pa)* K=* C HF (p+) = F (p) = 0

M g[ jPa C E[57¨E[ C 'PQ?)¨ ;X?HIEFH'E(Pa)*jl![ &([aX)* H 5)*P ¨?dkE[d-()E&(v C FTE[ C 'PQ?)Y% ;X?HIEFuH'E(Pa)*E[Qdk+DX)* H5)*PaY Y?d-(]E[d-()E&( hV 5)*P H C ;X?HI]ET7*E)EHI"E[aPa()*_H'E(Pa)* lE[adk+) E[aX)* H_ g[G' E[ =' C HIE C

l(p)FH)**! C

p C *'XXT

FP (p) ¥g[ " "*H C (Pa H N

XR'* Y?H'*]Qdk+DX)* H 5)*P [5+ kj_H\[5 C H(;\ C C &]H'\Pa)* ¨$ )* )*H .-(]H'E(Pa)*!(';!jE[ O dk=)*(P

U C E

EK O dkV M OGH C F ."H C 7*E)EHI

! !#"sbVdmq k#_u!u!a%qwrt_e"nVq `!_ `!bVa 9cno_e C^9i0!_onod e>noae"qwd `i _v7nodmq`!u!d $Vo`!d _eE · GP (p)

/d `!b5u!a%qwrta%ky`j`!_Z · FP (p)

~ ^ fl_u!a aeVau|cp vx_u!f[_vl(p; ·)

dYq d $ae'$ i \F: + 8J8)ce"n 1 :*89+.2 /%+.2 ;=>*>*?.'r~I&Y.#Ay~!%[#"sbVdmqdmq7a%cqwi `!_$au!d vxi-qwd e"k#a

l(p)fl_eV_`!_eVdmkcp p i:noa%k#u!a%cqwa%qSd e

FP (p)ce"n

FP (p)fl_eV_`!_eVdmkcp p i

d e"k#u!a%cqwa%qzd ep~

@


H'E(Pa)*%|[ &([GDX)* H 5)*Pak[ PaX)*<-(Ë[ )* .E'57E C k .E[ CEK O dk M V[ &([G

X)* H5)*P [5E[QEPa]X)*(5 DN(;\ C C &aH'E(Pa)*(';U a<k+DX)* H

5)*Pvw'5?* w';¨k .E[h C C H)** C &"X)* HE[*H C FWH\[5 C HY*[)* C w¨()H\[5 C &(E_E["H C E)E)N*_E[57gE[5)*P(* .EgH'E(Pa)* C H(PaX?IE .E C k .E[dkj) DX)E .H5)*Pa A 7gR+E[)* C *)*H\[ZNHIE'5¬H'E(Pa)* 5 *

λ1 = 0;E[ C

FP (p) = 0

FP (p+) = 1

κ1 = 0

C Fl(p) = E

Z

? * 5\[] ;X|HIEF C 'PQ?)H C *'Pa)*YX?) 5)*P gE[!EPa =() 5)*Pa 5)*&Z)*F*E[!X)*wF'HIYX)* H"E[INt;¬) ADC E[)gk+()*F E["H C *'Pa)*Y)* ' C .=()*Pa NhF \)* ';EFH)*(*5)*Pa `%)*GF'H C &E[ &(GwFuH'*"H C \ C "Ph)*&( C H(E

γ C VYPa C &5)*Pa X)*GF'HIE C

H(EQPhN F Z;¬)] C F )*hF E)* ';EF HH()*F C &ETE[hH'PQ'R7E .-(aF C * .DN =' C HIE CΩ0(γ)

k .E[ C 5PQ'Pγ0≥ 0

C F *'X)*PQ'Pγ0 `%)*GF'HIE C H*E_)***'PaF E

[5d-( C .EQPa C ¬ E EΩ0

[γ] < ∞ Ω0(γ) YE[QF .*E)* ';E . C

γE[57X)*I-7 Y .

+,! ,!$#$&Y 'HIE .-(5)*PaY[5-ZQ C E)*F©E[QPh)*I Yg[]HIYE[57 5)*P t;¬)* .E&(GGF7 H)\ C X)* H

p ≤ ϕFG C &('5)E C E E[57gE)EFk ?\"XRH %V 5)*P

k .E[X)*GF'HIE C H(Eγ gHF5)*PDNGX?

γ

$ )*Pa)*Y**'PaFaE]Ph ; Pa +E[ )Ph)*(I¨*[5)*wk[ H[h w' .-7 C E]Ph ; Pa C & E[ )EF;NZD\7EX)* O dk .?Ph)*&( C GH(Ej)*gH C \ C L ;X|HIEFWX)* E)*&( .-( C ZN

π(p, γ) = (p− γ) · l(p), K JG @dcNM

k[)*p−γ

Ph)*&( C 7X)* j C Fl(p)

)EIX)EIE C EË[ ;X|HIEF C 'PQ?)vH'E(Pa)*&( .-( C ZNL%w'57E C K JG nNM .¬H C *'Pa)*Ph ; Pa YE[ ) ;X|HIEFTkj.E[T C FTE[)X)* H)*¨F E)* ';EFQHH()*F C &E

FP (p) ij C *w' C E.N w5)*P Fw C t;¬)

X)* HY?dk .EjPh)*&( C 5H(E+?H'* X)* E¨kj('FW?H(Pa C &Z7E .-Z VFF .E C . N )*F;NPa C E C F E[~Ph ; PQ'PbX)* H©t;¬)Fw C ;HF\[©H C *'Pa)* )**)-7E C X)* HI5 *

p ≤ ϕ

V C H*E)N H C F .E C =() X)*wF'HIE C K=*'XX.N M ]E[57ProbΩ0

(γ < b) > 0%k[ H[

C *')*TX?(* .E .-(u&Z C W=)*(P,E)EF g[ PaX. .WE[57=()b = γ0

*(Pa,5)*Pa&(! f "sbVdmqdmqcq!qwVfla%n7vx_uzk#_e0$aeVd ae"k#a~ #Ce"q`!a%cn9'

γk#_Vpmnhcpmqw_ $taIcSk#_ q` + &%('$gnoartae"nod e._eh_o`!rVo`_ugc `!a%k|bVeV_p _*i*'9u!a%qwrta%ky`!d $ap i~ ^Dqc k#_e"qwaa` Vae"k#a*'Dc "u!f" q'$tab"c#$d _Vu fhci>k|b"ce.a*'9r"cuw`!dmk#Vpmcu!p i

d vDd `|q7fhcud e"cpk#_ q`|q cu!ajd e"k#u!a%cqwd e. $ a%kcVqwaj`!bVau!a dmq c kcr"ck#d ì-k#_e"q`!u|cd e ` /d `!b u!a%qwr a%ky``!_)rVu!_ V`fhc*0od fld %c`!d _e~

ZJ


5 C w)*'X; .bFH)** aF )*HIY5 C w)*'X;EHIN=(dk+=()

b > γ0 C F 5E[G' |Ph)*(I

E)*'HIE')*!FG C H[5 C &(7 Y C E"E[ *'X)*P 'PH(X)*GF'HIE C E[57dk C C C &Z7E .-( X)* EZN

γ C F

E[!H'P 'R<\ -Z F C * .DN=' C HIE C X)*GF'HIE C H(E&8 !$#Y5)*PaZNΩ(γ)

+g[ C Ω(γ)

H C |" ;X)**EF© C E)*PaΩ0(γ)

Ω(γ) =Ω0(γ)− Ω0(γ)

Ω0(γ),

k .E[γ ≤ γ ≤ minγ0, ϕ

A =(dkjE[57gE["Pa*')*"HIE .-( 5)*Pa

Z5 g C F(&( C ('

Z = Z0 · Ω0(γ),

k[)*Z0 +E["Pa*')*"75,! ,!$#$&Y 'WH\ -Z 5)*Pa

VY 5)*PaW Pb7W C H)** C & E[ )aPh)*(Ih*[5)*©?IH'*~ E[TH C \ C Ph)*&( C X)* E 5E[INTPh ; Pa "X)* E&( .-( C E[ )X)*GF'HIE C H(E A YX|(** !E[57E[hEPaaX)* ]I-ZH C ?WH\[ I-(F 7]F Z;¬)* C ]X)* H g[w' 5)*Pa!+E[hEPaH(" NGX|aPhN~t;¬) F Z;¬)* C "X)* H ag[ "Pa C E[57! F C E H 5)*Pa"PhN©F Z;¬) CE[ )jX)* H C &]*E)E7E&( . %g[ *Igl(X;E Ph|E)E7E&(

Sγ;H C \ C ¨\[EY-7'+

pE[57Pa ; Pa X)* E C F g&( .-Z C ZN

Sγ = arg maxpπ(p, γ)|γ ≤ p ≤ ϕ K JG @(@VM

k .E[

π(p, γ) = (p− γ) · E

Z0 · Ω0(γ)· 1 + κ1[1 + κ1F (p)][1 + κ1F (p+)]

.

A H C E'P_)*+)* C jdk+F E!H\[5 C &(E[ )*'XX ) ZE[ )**'.¨ w' .-7 C E"E[Pa C (X?(.N*(';E C )=-A F J1B5X\K @dn @VM A C H C E'P_)"H C P_X)Ed-(Q[ * .E'57E CK O <k )* M E[ C

λ1 = 0¨ C F E[)*I=()*

κ1 = 0 S ; Pa C &TX)* EQPa C

Ph ; Pa C &TE[F Z;¬)* C Hp − γ

k[ H\[¥[5_ .E_Ph ; PQ'P 7 E[[ &([aX?(** X)* H g[w' |X)* H)* Pa C (X?(.NhX)* H 5 *

p = ϕ=(). 5)*Pa

! 0Vk#p "nod e.`!bVahkcqwa `!b"c`crt_ qwd `!d $a fhcq!q1_v "u!fhq1b"c$aγ = ϕ

$ a%kc"qwa7`!bVaeF'TrVu!_ V`|q z_Vpmn$taau!_hce"nc "u!f _Vpmnb"c$a au!_lrVu!_ V`|qsu!a% cu!nop a%q!qz_v d `|q/fhcu!a#`/qwb"cu!a~

(e


A κ1 > 0

C F¥E[*ISγH C \ C aPa()*E[5 C C X)* H 5)*Pa_k +? C F Z;¬)* C

?IDk+I C E[a.E) C 7E .-( X)E .H C &E)E7E&( WjI=()*_ C E)* C &E[_Ph)*(I 5)*Pa"[5-ZEaH\[G(*!_X)* H *E)E7E&N A **'PaFE[57 5)*PaX';X)*(5 E .gNGPaPaIE)* H N C H\[Pa C _

Sγ g[ C g 5)*P _E)E7E&N _H\[5)EHIE)* F¥wN uX)*(5 . .DN

F E)* ';E C d-Z)SγZ=)*(P k[ H[a C Pa C H\[(* C ?I=()* C E)* C &"E[Ph)*I

Y C EQZNF (·; γ) E[QE)E7E&N=() NGX? γ 5)*Pa ?k[ .H[© YhX)*(5 DNF E)* ';E C<-()+E[ *ISγ %g[" C F .-G F'5¬X)* H\)E7E& gH C ?!&(&()*&Z<\IFE E[ X)* H t;¬)

F E)* ';E C

FP (·) =∫

γ

F (·; γ) · dΩ(γ). K JG @ J M

ADC E[ k+N (E[jF E)* ';E CF (·; γ) ?H(Pa C FX? C F C % γ *YE[57 FP (p) H C \ C FPa .*EFX)* Ph ; Pa C &QX)* Hg=()vX|(** H(\7E

<=:0: GJI;R1D > BHECACEI6ECB

ADC E[Q=(dk C &WF C .E C ¬E[_?[5-G (') jH C *'Pa)*! C F 5)*Pa")* H(PQ C F~EF*H)* ?hE[WPh)*IQw' )* 'P TL%w'5.N *(PahH[57)\7HIE)* \ .HQgE[Ww' .)E .'P)*"(';E C Fv

. s>694<6=2?>o / 2& != "#Y # #Y"2 # &!$# (ϕ, γ, F (·; γ), γ ≤ γ) _!Y*6&!

!Y*, # !$# "!$#% /. #% H #Y)!Y*,3123'_#

FP (·) =∫

γ

F (·; γ) · dΩ(γ),

, ' J2 J#Y!Y* , !$#% !Yγ ≤ γ0

& H&8 !$#Y & !Y*, # !%# "!$#%/. !Y*, #Y !Y #

Ω(γ) =Ω0(γ)− Ω0(γ)

Ω0(γ),

! a^Dq!qwVfld e.l`!b"c`/`!bVau!acu!aSqwa%$au|cp rVu!_ V`9fhc*0od fld d e.hrVu!dmk#a%qsdmq$au!i aeVau|cp ~ #Ce b"cro`!auld `S/d p p$ a1r _d e`!a%n_o`9Ve"noau/bVdmk|b k#_e"nod `!d _e"q

Sγ = S(γ)bV_pmnVq%'od ~wa~./boae c VeVd ` VaSfhc*0od f7Vf a10odmq`|q~ aa

1 2989+ ]5bD/Ia#`Dcp ~F; . . ..'r~D.#G ' u!_r _ qwd `!d _e @Ay~[ aa 1 2989+ ]5bD/Ia#`Dcp ~F; . . ..'r~D.@Ay~

U


ϕ

# " "2 ! , ! J2 &77 7 &! *6&#%" ;#

ϕ = b+ (λ0 − λ1)

∫ ϕ

p

F (x+)

ζ + λ1F (x+)dx, and

!Y*, !$a&! 7' /. &"* !$' γ

J2 # ! a&823 ' a& & #%1. 2 & #Y #Y!$' # !$# "!$#%

F (·; γ) !Y*6& !8"!Y5, #Y!$#YT & #Y #Y!$' _!Y*,; !Sγ

/.+ J! 2& #Y23# #Y"7#% /. !$',

γJ2 H7#Y !Y*, J2 & "2 !$a&! 7#% ;#

Sγ = arg maxpπ(p, γ)|γ ≤ p ≤ ϕ

J#Y!Y*π(p, γ)

8J1 '3 6&!$#%

ADC H XI? P/P C F E J1H P ?BV?B K @dn(n M GE[ w' )* 'P +F*H)* ?F C FI\ . g[INX)*<-(WE[57 E[)* ~' C w'*(';E C A Y . **'PaF E[57QE[)*)*HIE .-(H' E(Pa)*k[Q*)*H\[X|)*Ph C C E.N K= *

λ1 > 0M ; C w' )* 'Pk .E[W C C DF&( C )E7E

X)* H_F E)* ';E C !)*('](';EH(Pa ag[ "[(F =()"[(Pa(&( C ('] kj¨ =()[IE)*(&( C (' H C *'Pa)* !g[ H C F .E C E[57

λ1 > 0 C IH*\)Nu C F~*' <aH C =()

(;\ C C &Q C C DF&( C )E7E X)* HF E)* ';E C w E G .+FG C gPh7*E)¨k[IE[) 5)*Pa)*_[(Pa(&( C ('"() C _g[aw' )* .'PX)* H F E)* ';E C

FP H C E C '('" C F

[5 aH CC HIEFu*'XX?() Yg[QPh ; PQ'PX)* Hpw'5E[QH C *'Pa)* ¬)**)-77E C

X)* H g[QX)* H]F E)* ';E C FG C Y[5-ZQ C NTPh*X?( C EY|H'* E[)k *!E[X)* H t;¬)*F kj('F C ?X)* DPh ; P_ C & ~g[ Q=(.dk]=)*(P E[**'PaX;E CE[57

λ1 > 0 A

λ1 → 0E[W(';EH(PahH C -Z)*&(]\E[WPa C (X?(.Nu*(';E C =-A U

F J1B5X K @dn @VM J1B P ? WI_ K J c(c(c XXv e @ M E[dk*(Pah PaX .H7E . C !gE[w' )* 'P *(';E C X5)E H'R)*.NuE[W C O ' C H

λ1 A E[W)E7E7Qk[ H\[ HIE'5

H'E(Pa)*+)*H .-(E[)+X)* HYt;¬)*j C H)** 9K=R)*&( M 5)*Pak .E[WdkX)* H¨k |[5-Z C F;- C \&(h C FuE[ )"H'E(Pa)"5*a C H)** WVgFF .E C . N E[_X)* E!+R)*&(5)*Pa¨ C H)**Y C FaE[(*Yv*Ph 5)*Pak .E[h[ .&([)¨X)* H¨FH)** g[ ¨Pa C E[57E["R)*&()

λ1 ;\[ &(&())* E["F Z;¬)* C HI C 5)*P* ! C FX)*

ADC H C H'* C E[_PaGF C H()*X?()E7EE[ =(dk C &W)EIR7E C *[ X A + ." "**'PaFE[57E[)*])*![IE)*(&( C (' 5)*PaY C FT[(Pa(&( C ('H C *'Pa)*k[h*)*H\[©*w' C E R N=()lgdk X)* Hg\%X)* H%F *X?)**F]w' )* .'P )* *?H'*j(H C *'Pa)**)*H[ % * H C *'Pa)*Q*)*H\[ )*&Z)*F*]gE[ )]\7E' ~$ )*Pa C I-()Qt;¬) TX)* H?d-(©E[TH C *'Pa)* +)**)-7E C X)* H 3L%w'57E C K JG nNM *[dkWE[57HH()*F C & E

Z^


E[_*X|H 5F )*R7E C *[ X©?IDkj C FPh C F C FuX)* HR)*&(5)*Pat;¬) dk+)X)* HE[5 C *Ph)5)*Pa VYNGPaPaIE)* ¨ C 5)*P* C FhX)* E¨ C H)**+7HIE'5?H'E(Pa)* *)*H[THIE .-G .E + C H)** ADC E[ C GH\[5X;E) |E[!* P 'R<E . C PaGF k[ H\[T YaN C E[* YE[!I-Z';E C )NPaGFG ACB P ?H K @dn U M C FQE[|<-(+F*H)* ?F_*)*H\[_PaGFG J1B P ? gI¨ K J c(c(cNM )*QX)** C \IFv ]g[ )**'.E %E[ * PQ'R7E . C C F©E[ ))*R7E C EWPaX )* HF57\_)*"&( .-( C C ij[5X;E)U

(

3

A cynic might suspect that the lack of empirical work reflects a lack ofinterest in the real world on the part of those concerned with search rules.A glance at the authors ... suggests that this is not the only reason. Itseems to me — and my interest in such matters is admittedly casual —that the problem of determining characteristics of search rules empiricallyis a very difficult one. X $

( ' *+-,/.103254567,980:+

ADC E[ H[5X;E) ; C IkPawF| ¨X)** C EFv A jH(PQ C E[YPawF 5Fa*)*H[WPawF|J1B P ? +I% TK J c(c(cNM X)** C EF_ C OGHIE C JG ek .E[!E[jI-((';E C )N * P 'R<E CPaGF% ACB P ?H K @dn U M _g[aH(P C 7E . C )**'.E" C C I-((';E C )N©* P 'R<E CPaGF C k[ H\[_E[Ph)*IX)* H C ¨ E C &(gX)* HZFIE)*Pa C FaZN w'57E C &!&(&()*&Z7E *'XX.N©k .E[u C &(&()*&Z7E FPh C F~=' C HIE C ADC EF lH[,5)*P ;[ .E *(PaPa C (X?(.NX|dk+)Y|H'*QH C *'Pa)*)* C YH(PaXIE.N C =()*PaFT?(';Y*.)*Y C FE[ X)*GF'HI X)* H ]LH\[,5)*P H[5)*&( .EY<k C X)* HvFX? C F C &Ph C .N C .EY* H("E)*'HIE')* C F~ C H C *'Pa)* vX)*I=)* C H] C Fu*)*H\[uH(E _i¨ C *w' C E.N E[Ph)*( gH\[5)EHIE)* FZN C C DF&( C )E7E"X)* H F E)E .';\ . C g[a=)EPaIkj()*©jE[aPawFX)** C EF C E[ "H\[5X;E)! E[aI-((';E C )N~* PQ'R<E C PaGFv ACB P ?H K @dn U M ;k[ H\[T g5*FT C ( C gkj()*ZNTOG F C INW C E) C F H\[5)*FT* C 5*'PaPh)* F C ?R VJ1B C F ACB P ?H K @n ZJ M g["PaGFv ACB+UP ?HUK @dn U M .E*.¨ C "(';E C F~[)*_ C .E()* &( C -Z)** C ]g[ C C H*E)N?H'* .+H C E .E';E+E[Y=)EPaYE[ [ZNG)* FPawF G E wE[ GE C * C , ACB P ?HK @dn U M ZNWE[!XX)*ZH\[ J1B P ? !IY /K J c(c(cNM Gk[ H[ gF*H)* |FT C FI\

Z

e; @ ADC E)*GF'HIE C ? E J XI?R

g[PaE .-7E . C EH(PQ C E[*DkjPawFv 5*F! C E[%=(.dk C &+H C * F)E7E C $ )* E[ ]H(PQ C 7E C dk!E©F)EkX?( HINuH C H'* C Q C H C *'Pa)QX)*EHIE CE[57* \uF;N C Pa H©;¬HIE C C F'E)* RYFI-((XPa C C E HH' C OGH C F C E[PawFg J1B P ? Ih hK J c(c(cNM %E[X[ C (Pa C C YF *X?)**F¥X)* H_ ;XR C F]k .E[QF Z;¬)* C %X)*wF'HIE .-G .E E[ 5)*Pa ('; .Fw C )*I-(GE[+*(')*HE[*+F Z;¬)* C H C E[jH C E)E)N J ACB P ?H K @dn U M 'H F57E[dk 5)*P3F Z;¬)* C H)* *!wN CC d-7E C |';YE[)*+5)*PaY)*]|(' C FF©Eh*lE[ )X)*wF'HIE 7a&( .-Z CPh)*(jX)* H g[ ¨**'PaX;E C *Paj PaX'* .Z|H'*YE[ C H C E .-(E! CC d-7E=' C F5Pa C \.N FX? C F C E[jX)* HDHI(Ph)*&( C C F 7E[)*I=()*( C E[¨Ph)*(IX|<kj)5)*P Tij C *w' C E.N %|E[ PawF!H(PaXPa C !H[ E[) =() C C DF&( C )E7EX)* HF E)* ';E C H C 9E C ?Y(*)-(F C F G .v CC d-7E C & w5)*P ;X?HIEFWE]?E_H[5)*&( .EgF* )*FX)* H g[ )*F I-( C . .g*PaE_|"' C '*'5vEa P_XPa C C w' )* .'PPawF C ET C I-((';E C )N~* PQ'R7E . C PawF ."*[('F ?aX;Q CPa C F E[57 ACB P ?HK @dn U M '*h C wHR** HgPh)*I_PaGFjEu\ *[¥~*[())*' C w' )* 'P $5')E[)*Pa()*¬ . C H*E)N©E[57 C w' )* 'P H C HX;"?Q'*F?H'*h*'H\[ * PQ'R7E . C PaGF.k+NG"H C * E!jDk+X5)E]*[()!)*' C EF;N\7E; C F_E)E C * .E C )*'%E[57¨FIE)*Pa C [dkE[H C (P]N Pa<-(=)*(P C \7EEE[ C G $5(')E[.N CC d-77E C )*_Ph ()FIE)*Pa C C jH C (Pa HQ&()*dkgE[ l C F . g*[<k C C E[ gE[* gE[57H C *'PaI)EH C C O ' C H! CC d-7E .-("HIE .-G .E + 5)*Pa C F Ph)*I E)*'HIE')* g[)*I=()*E[ QPaGFj GE C F_E[W=wH'QEu C .PaX?()\ C w'E C C F'E)* Rv()*&Z C 7E C k[57FIE)*Pa C Ph)*IE)E'H\')* a*'P'X H(PQ C C &Y?E[ P_GFt;¬)*E[+X?(** N"? C kj)* C & w'E C |(';E[+;¬HIE+E[aRH©g C =()*Ph7E . C C |[5.gjE[hH C *'Pa)* %"kj¨"E[hE)E7E&( !5)*PalE ;X( .E[*¨=)* HIE C A lFPa C E)E7EF][dk E[¨Ph)*IE)*'HIE')*¨FI-Z(Xk .E[)*&Z)*F¥E E[T*)*H\[ H(E C F[dk E[*~*7)EH\[ H(Eh C O ' C H© CC d-7E .-(HIE .-G .DN Ph)*I_H C H C E)E7E C j C F 5)*P D* WF E)* ';E C g[* PQ'R7E . C )**'.E*W .'E)E7E!E[QF Z;¬)* C PaX5HIEY¨H C *'Pa)* v C =()*Ph<E . C C 5)*PaF Z;¬)* C * C F_t;¬) C ;XR C 7E C =()%[dk 5)*P D* +F E)* ';E C %)* * g[*Y C F =')E[)* P '7E . C )**'.E)* X)** C EFT C ij[5X;E)U

(

e; KJG g[ S GFOwE)*'HIE')* ? E J XI?R

( 032 ,/.14567,D4 .

g[Ph C ( HIE .-(W ACB P ?H\K @dn U M .!\© C -(E &Z7EOGH\[G'PaX|IE) w'E C [<k CC d-7E C ")*_&( C )E7EFv W¨N C .NG* C &W kjF E C HI" CC d-7E C )*&( Pa E[ C E)*X)* C ')* R7¨ C F~E[_)*(';E C F~)*&( Pa X ." *[dk C E[57"?E[ F~EF Z;¬)* C (';EH(Pa ADC E[ E'F;N l C .NTE[ C E)*X)* C ')* R)*&( PaQ ¨ C \I)EI* vk[)*_X)*7H* CC d-7E C j)*' C F)*EGGF C k EH[ C ((&( .+ C H C E)E+E PaX)*d-ZIPa C EjEH[ C (&Na C E[YH*E[)*(';E C Fh)*&( Pa $ F¨lPaX )* H|XX H7E C PhN? C Ik Ph)*(IE j*'H\[ aH(PaPQ' C H7E . C C F C =()*Ph7E . C EH\[ C ((&N ¨k .E[Pa C N*Ph C FuPaF 'P * F,5)*Pa H(P_X?IE C & C F~X)* H-)NG C &H C * F)E.N( QjIE .FE[E'F;N E[ CC <-77E C X)*GH* ¨E[H C E)Egw'I*E C FF)***F C E[PaGFX)** C EF [)*© h[dk H C *'Pa)W|[5d-G (')W";¬HIE 5)*P |[5d-G (')W C F +E[)*I=()*Ph)*((';EH(Pa g[ OGH\[w'PaX?IE)* R C H(PaX?IE .E C PawF ACB P ?H K @dn U M H C ?!F*H)* ?FT)* O Na=(dk $ )*h" jE[T C F'E)N _=(' C FF ZN C 5)*P Pa C (X|( ADCE[a*'*w' C X|)* GF lE[a C F'E)NuFI-((X!E[)*('&([ C E)* ] C F ; .E!GHH')*)* C & C H\[ X?)* wFuF' E&( C )E%H C F \ . C C E[_ C F'E)Nu C Fu .E [ E()N( QVY 5)*PaX)*GF'HhE[WEPaa&(GGF ';QF Z;¬)] C X)*GF'HIE .-G .DN( Tl~ C H)**aE[ )]X)*GF'HIE .-G .DN 5)*Pa C &Z&(+ C E F *Hd-()E[ )H(PaX?IE .E()* <EH\[ C ((&( hK= Pa \7E . CM C F C IkEH[ C (&( jK=X)*GH* CC d-77E C M g[gPa(% C E)*E C &=7E')*+|E[gPaGF; E[57E[Ph)*IlE)*'HIE')*¨ C F E[|[5d-G (')wE[ 5)*PaFI-((X! C F(&( C ('*.N 7FX? C F C & C 5)*P [ E()N C FT .E C -G )* C Pa C d ¨[57YH C ?!(*)-ZF© g\["E Pa X57E[TPhH)*]H C (Pa H-7)* R G*'H\[j(';EX'; ;I-(?vEH[ C (&( H| C dkF&( C 'P |)/5)*Pa 5+kjv+E[E PaYX57E[Pa H)*wH C (Pa H-7)* R ;*'H\[T5)*P X?( HIN .E *'HH* ¨ .E]Ph)*I *[5)* C F .EQ .=IE .P_ ©V9E)]E[WPh)*( [5FI-ZI(X?F=()_H)\ C E Pa;E[!Ph)*IE)*'HIE')*!'*'5.N*I*E*_E[57E[)*! )*R7E .-(.N!H C \ C C 'PQ?)-5)*Pa C E[gPh)*Ik .E[ *(Pa 5)*Pa ; .E C &" C F E[)* C E)* C &]E[Y C F'E)N( Y Z;¬)* C +)**'.Eg)*Y(;\ C Fh=()¨E[YDkj CC d-77E C )*&( Pa * E[Ph)*I_E)*'HIE')*-)* a7HH()*F C &uEu5H\w&()*(' C F¥H C F .E C _";¬HIE C &~E[C 'PQ?I) C F* 5)*Pag C E["Ph)*I

] Vuw`!bVau9noa#`|cd pmq/cu!ad $aed e&$"qwa%ky`!d _eV~ o~ #..'r~D? .V~ _usvxVuw`!bVau9noa#`|cd pmq%'Vqwaa 36572989+.:<;=>*?&X0AzceVn),+.-0/1 2)ce"n 36572989+.: ;=>*?@ 'r"cuw`G*Ay~

n


0:%<=:/9 QHR G;S"ECP D"I6BHP DBI6R

g[TP_GFg _H C E)*'HIEF C F *H)*IEE Pa%k .E[ E PaW=() EH\[ C H)** C a? C & C E)*X)*IEF©*hE[57Y C ]X?)* GFT E[)*QPa C E[ ? E ?aN()YH C * E%UWX|)* GF A **'PaFE[57 C H\[X|)* GF

tE[)*" g C .E C 'PQ?)

Zt

* C &(DX)*GF'HI 5)*Pa ?X)*GF'H C &Q[(Pa(&( C ('+&(wGF a_HH(' C g=()j C F .-G F'5!5)*P[ E()* GE[*Il C F H+HIE .-( 5)*Paj C X?)* GF

t jF C FZN Zt

$()j PaX Z0 = 1, . . . , Z0k .E[uE[ C 'PQ?)" 5)*Pa" C E[_Ph)*(I! C X?)* wFt| C &&( .-( C wN~E[ C 'PQ?)"

Pa C E C Zt

%=()Q C \ C HZ0 = #Z0

$5() 5)*Pi C X?)* GF

tE[ C .N C X';

C FF=()gX)*GF'HIE C gHX .\Kit

k[ H\[FX)*H 7EY7 H C \ C C F'\)NZk .F)E7E

δX?)X|)* GFv %g[ 5)*PaF Z;¬)+ C E[ )g* 5Pa*')*F C E)*PaHX .\¬EGH\

C E[ )%X)*GF'HIE C EH\[ C w' C Fa C E[ ) X?( H Y Z;¬)* C H¨ C X)*GF'HIE CEH[ C .w'")*!)E O HIEFuZNE[]X)*wF'HIE C H(E

cit|k[ H[~)*!H C \ C X?)Y' C .Y

(';EX'; $5()E[ X)*GF'HIE C =' C HIE C =()H\[ 5)*Pi . **'PaFuE[57 E[ (';EX';

Qit

C X?)* GFt X)*(X|()E C ?E_E["HX .\vEGH\|

Qit = A ·Kit,

k .E[A? C &]H C \ C gX)*wF'HIE .-G . N( \|*'XX.NhvE[Y C F'E)Na C X?)* wF

t ¨E[ C

&( .-( C ZN

Qt =∑

i∈Zt

Qit.

`%)*GF'HIE C H(Ecit 5)*P

i C X?)* wF

t)* H(PaX?(*FE[ -)* R C X';gH(E

γitvk[ H\[ )*Q*X?H 5HQEH\[,5)*P ¬E[Q C F'E)NZk F )*IE') C C HX .\

ρl C F©E[

FX)*H R7E C )E7Eδ * ¬E[ X)*GF'HIE C H(E"X|)"' C . HX .\j5)*P

i7 E Pa

tH C ? k)* .*E C #

cit = A · γit + ρ+ δ. # `9dmq9k#_e@$aeVd ae `s`!_jcnVnod `!d _e"cp p i cq!qwVflaI`!b"c`9`!bVa __on dmq9clqwau$dmk#a1_u/rtau!dmqwb"c$Vp a*'Vqw_l`!b"c`9d `Dkce

_eVp i $ aSk#_e"qwVfla%nd e `!bVaSr au!d _on _v rVu!_Vno"k|`|d _e~ #Ce`|boa,36572989+.: ;=>*?&X0Afl_onoap`!bVa "u!fhq9nod / auDd eg`!bVad uDrVu!_ono"ky`!d $d `i $Vo`9`!bVad uDrVu!_ono"ky`!d _e k#_ q`|q

cu!a dmnoae `!dmkcp ~ #Ce `!bVa eVa% fl_onoapD_o`!p d eVa%n bVau!a*' "u!fhqhb"c#$a dmnoae `!dmkcpDrVu!_ono"ky`!d $d `!d a%q$Vo` $cu!i d erVu!_VnoVky`!dm_ek#_ q`|q~!%^9_u!fhcp p i*' `!bVa%qwahk#_ q`k#_flrt_eVae`|qSkceVeV_` $tahqwVflfhcu!d a%n d e:`!bVdmqsc%i%$ta%kc"qwa

γitnoar ae"nVq1_e

`!bVag_o`!rVo`'zce"nρce"n

δcu!afla%cqwVu!a%n rtaulVeVd `jkcrVd `|cp ~ au!a*'d `hdmq r _ q!qwd $Vp acqlc:qwd flrVp ap d eVa%cu

rVu!_VnoVky`!dm_ejvxVe"ky`!d _egdmq9cq!qwVfla%nN~

c


VY¨ ;XR C Fa C OGHIE C e; KJG U ZE[ C F .-G F'5H(jH(PaX? C C γitH C ? C O ' C HF

wN];¬()E% C ] ADC E[g C F'E)N (E[j-)* R¨ C X';%H(E)*gF .*E)* ';EF HH()*F C &E H'P 'R7E -ZF C * . N"=' C HIE C

Ω(γ) l\GH(E| 5)*P H C * 5E[jX)*GF'HIE C

H(EX'g ;X? C F .E')* C ] $ )*P

i X)* E

πit C X?)* GF

t)*"F C F©)*I-( C '!Pa C '+H(E | *

πit = Pit · qit − γit ·Qit − (ρ+ δ) ·Kit − (rmit + rnit) ·Kit,

k[)*)*I-Z C '¨FX? C Fa C E[*(F_Pa(' C qitE PaE[ C F .-G F'5GX)* H

Pit+5)*P

i C X?)* GFt ij(EjFX? C FW C E[5)*P ¨HX .\5EGH\ ; C Fh C E[X)*GF'HFW' C .E

QitE[ &(GGF ¬k[ H\[uPhNTF Z;¬)Y=)*(P E[ *(F~' C .Eqitvk[)*

qit ≤ Qit

!\H*EH C * ¨?E[g-)* R+ C X';H(E

ρ C F

δG C F E[ ;X? C F .E')*¨ C k[)*

rmit C Frnit)*gE[)E7Ev Pa \7E -( C Fa CC d-7E .-( ;X? C F .E')*¨X?)' C .HX .\

&(d-Z) C FwN)*(';E C )K=FH * C )*' M %g[*Q)* ;XR C F C OG'*HIE C e; KJG KG g[5)*Pa_HIa C Dkj \&( $ )** %E[EH\[ C ((&N FIE)*Pa C Fv ADC E[*H C FEX |&( .-( C EH\[ C ((&N C FHX .\ 15)*Pa 5FH .F]7gk[ H\[X)* H E[INWk ¬t;¬)gE[ )(';EX'; g[h*'HH*Q 5)EP F')* C & .E" .=IE P_ !Pa*')*F ZN -7)* R_HF X?)=()*Ph C H

Xit

| C F gF C F© Pa<-G C &_-()E&("X)*GH* 5)*P X)* E

Xit = θ ·Xi,t−1 + (1− θ) · πit, 0 < θ < 1.Ke; @VM

ADC ()*F) EFIE)*Pa C E[_ CC <-77E .-Z X?E C E RjE[_ C F'E)N lE[_ ;X?HIEF -'%X)*GF'HIE C H(E

EΩ[γ]Pad-ZEaE[]I9YR7E C Y C dkF&(

Lt

C HI)E* ij C *w' C E.N5 CC d-7E C &5)*Paj[5-ZYE[X?(** DN_F *Hd-()* C &5K DF)Edk C & MC Ik EH\[GC ((&( jk .E[<kj)gX)*GF'HIE C H(E

0:%<=:%< @;FHS"B R+I RTQHG ?=EC@JI

ADC E[ !*'*HIE C E[a\7Ea-)* R =()!H C *'Pa)*Q)*aF C Fv g[)*7)ENt =

N ∀ t H C *'Pa)*¨ C E[Ph)*I Zk[)* Et

¬E[P)*HI'*E(P_)*¨ H)\ C *'XX ) C X?)* GF

t C F \[WE[)*

Ut

)*WH C *'Pa)*]k[uI .E[)QF F C Ph C &(aE C F C NW*'XX )g()gk[ k+ C Eh *'XX )+E[57[5FT)*F;NW*(F(';()+k[(*!*'XX )

[ _uXi,0 = 0

za7b"c$aXit = (1 − θ) · ∑t

j=0 πi,t−j' d ~wa~"`!bVa7r auwvx_u!fhce"k#aSdmq9`!bValqwVf _vcp p r"cq`

rVu!_ V`|q zad b`!a%n'$i cegd e"n"q`!u!i0 /dYnak#_e"q`|ce`θ~

@


[5F 'Q&( C W5 C w)*'X; ujE[ DNGX? H C E'P_)* KE C F

UM .kgNG]*)*H[ %';

E[ ) *)*H\[ C E C * .E F Z;¬) aij C *'Pa)*"¨ NGX|U*)*H\[ k .E[u C E C * .DN

λ0tl C F

H')*)* C E.NQE7E 5FaH C *'Pa)*K9 NGX|EM *)*H\[_k .E[_ C E C * . N

λ1t(k[)* .% **'PaF

E[57λ1t ≤ λ0t

ij C *'Pa)*T7)E~[(Pa(&( C (' g[ ))**)-77E C X)* H

ϕtFX? C F C E[~*)*H\[

C E C * .E Iλ0t, λ1t

GE[ C H(PaY C F 6bt;E[X)* Ht;¬)+F E)* ';E C

FPt(p)5 C FWE[

5 C w)*'X;EHIN)E7Eζt A g PaX .H E Nh&( .-Z C ZN`%)*(X?(* .E C JG @ Xv ?^( 5

ϕt = bt + (λ0t − λ1t)

∫ ϕt

pt

FPt(x+)

ζt + λ1tFPt(x+)

dx,Ke; KJ M

k[)*pt

+E["dk+)g|(' C F\[ E'XX|()FPt

(p)

L%w'57E C Ke; KJ M PaX .¨\[5<H\[H C *'Pa)g C .NHHX;EQX)* H dk+)jE[5 C ()gw'5EY[ )**)-77E C X)* H V¥H C *'Pa)DNGX?

E C .N H\[5 C &([ *'XX )l .[j)*H .-(

X)* H"t;¬)gE)* HIE.NW?dk .EgH')*)* C C ADC E[ )*Ph C F)Y . **'PaF~E[57E[ *)*H[u C E C * .E )*QH C \ C * ¬*)*H\[H(EQF C !-)N <-()!E[WH')E*hgE Paa C F E[w'

λit = λi ∀ t and i = 0, 1 g[

H C *'Pa)*j)*Ph7EH\[Fa)E C F(Pa.N]E"E[5)*Pa G C FaH[ 5)*PH C |F)Ek C k .E[_E[EPahX)*(5 N( A Ph7EH\[F E~5)*P E[WH C *'Pa)]';NG HIE.N C W' C .]X?)X?)* GFv Q ';NG"=)*(P E[ *'XX ) ' C E [_)*H .-(] C t;¬)k .E[ dkj) X)* H ()' C E ?\[ 5)*P&(G5 C w)*'X; g[ QE[5)*h7EX|HI_E[57_F Z;¬)*Q=)*(P E[()* &( C ACB P ?HK @dn U M PaGF ¨N PaXP_ C E C & L%w'57E C Ke; KJ M C E~E[PawF ju C ?IDk+ C H C *'PaI) *6&#%8 C FT C F'E)NE)*'HIE')*] \ *[Fv Y C .NFGE["k C & C *gEhX5NFX? C F C C H(Paa C F *)*H[ H(E .] !*H C E C &( C ] C E[aX)* H!t;¬)*F C F C E[5 C w)*'X;EHIN )E7E ADC E[ "k+N H C *'Pa)*Q7F'*"E[ )!|[5d-G .(')"EE[hHI C F .E C C E[*'XX.Nh* F C E[H C \)E)N C ACB P ?H[K @dn U M E[)*")* C Q*'H\[ Pa E=()E[!X)* H gg[!H C \ C RE H .DNWFPh C F=' C HIE C C -Z(.-(g\[!)*I-( C ' C E[ C F'E)N.k+dNGg? C & E["EPa

f c`!au'od `9dmq/cq!qwVfla%nj`!b"c`bt = b∀ t

~ IaeVau|cp p i*'od `9f"q`9bV_pmn `!b"c`ba10Vk#aa%nVqz`!bVaSfld eVd f7Vf `!_`|cp

rVu!_VnoVky`!dm_ek#_ q`s`!_E"cu|ce `!aaIrt_ qwd `!d $aSqwVrVrVp i*'od ~wa~Prob[b > cit] > 0

~a^9p `!au!e"c`!d $ap i@'T_eVa k#_Vpmn-cq!qwVflal`!b"c` "u!fhq7cu!ahfhc`|k!bVa%n /d `!b3cgrVu!_ $"c$Vd p d `i `!b"c` noartae"nVq_e

`!bVad uqwd a*'sd ~a~zc-pmcua "u!fdmqjfl_u!agp d !ap i `!_ $tagvx_Ve"n $i c k#_e"qwVflauh`!b"ce>c qwfhcpmp9_eVa~ "sbVdmqqwap v7 aeovx_u|k#d e. a1/ a%ky`Db"cq $taae`!__hq`!u!_e. d e`!bVaqwd f7Vpmc`!d _e~

(J


0:%<=: R1DR+I ECFHECF DQHR )I6ECP1R

ADC \[ . C Ik3PaGF 15)*Pa[5-Z EaXE[!FPh C F* F" C Pa C F * ;E[INH C &()*<k C F~ ;X5 C F©E[ )YHX .\lEGH\T C .N .E[INLK= ;X?HI E M *lE[Qw'5 C E .DNTX)*wF'HFv C E[_HI C E)E)N l C E[_PaGF ACB P ?H K @dn U M ¬E[5)*Pa".kgNG *E[ k[(w'5 C E .DNuE[IN [5-ZWX)*GF'HIF¥ C F E[w' H C &()*dk )*)**X|HIE .-ZW GE) C ¨HIE()* g[Y C .N_H C E)E C j ¨ C E) C w * ZE[INa[5-(E])*Ph C k .E[ C E[ ) C C H R| P_ E=()g C -ZEPa C ADC ()*F)EWFIE)*Pa C "E[QX)* H]H\[ 5)*P H\[5)*&(Y=()Y .E(';EX'; ?E[QPaH\[5 C *P J1B P ? YIj K J c(c(cNM ¨ ¨XX Fv V5)*P)*H\[j .E%X)* jPh ; PQ'P .¬ .H C EI? .E+X)*GF'HIF' C .E ; * ; .

qit = Qit

%g[ w'5 C E . NQit

E[57gH C ? ;X?HIEFEQ?*(F C X?)* wF

tZN 5)*PH\[5)*&( C &_X)* HI

Pit g&( .-( C ZN

Qit = l(Pit) =Et

Zt

· d GPt(Pit)

d FPt(Pit)

=Et

Zt

· 1 + κ1[1 + κ1FPt

(Pit)][1 + κ1FPt(P+

it )],

Ke; e M

k[)*Et ·GPt

(Pit) E[ C 'PQ?)5H C *'Pa)*k[X5dN]YX)* H+|<-(

PitZt ·FPt

(Pit) jE[ C 'PQ?)g/5)*PajE[57t;¬)g X)* H ?d-ZPit5 C F

κ1 =λ1

ζt

% C *')E E[57+E[X)* ¨Ph ; Pa C & X)*(P?E[ 5)*P[5¨ ' C w'*(';E C ( . %)*w' )*F_E[57

Ω(γ) gH C E C '(' OG C HE[(';EX';a 5)*P _FIE)*Pa C F wN .E_HX .\+EGH\ jE[)*R7E C *[ X L%w'57E C Ke; e M '*F C -()**.N l * ¬=)*(P

Qit = l(Pit)=(dk

Pit = l−1(Qit) Qg[

=' C HIE Cl(p)

FHI)E*j Cp C F (E[)*I=()*G 5)*P

i 6= jk .E[

Kit < Kjt

C I-()H[5)*&("X)* Hg?dkE[57¨+5)*P

j g[)*R7E C *[ X vL%w'57E C K eG e M C F H7EE[57j 5)*P

\( C \hH C * F)E7E C E[QH C *'Pa)* v|[5d-G (') Kλ1M Yk+IYE[Q?[5-G (')

.EYH(PaX|IE .E()* KFPt

(p), ζM A *h*[<kYE[57 h*'HH**=' 5)*P Y)*Ik+)*FFuZNE[

H C *'Pa)*k[ C t;¬)* C &aa)*R7E .-(.NWdk X)* H +g[ gE[!*H C F©Ph()gF Z;¬)* C HE E["PaGFvE ACB P ?H K @dn U M ADC EFuw'5 C &h&(&()*&Z7E]FPh C F~ C F~*'XX.N v 5)*P X)* H]t;¬)

Pit YFIE)

Pa C FHH()*F C &QE_]*)*H[H(XX)*ZH[v %g[ + +)* O HIEF C L%w'57E C Ke; KJ M C FKe; e M %g[*"w'57E C g)* *'E .E';E C &QE["**'PaX;E C ACB P ?H K @dn U M E[57+E[H C *'Pa)*_)*WH\[5)EHIE)* F ZN ©' C .QRE HW&(&()*&Z7EWFPh C F HI')*-( g[ Q -Z)N *[()F*H)* X;E C ?H C *'Pa)* w|[5d-G ') A %w' .Eg)*E)* HIE .-(+E!**'PagE[57#aa a%ky`!d _eo~ .'rVr~IG*Go~

e


H C *'Pa)*)*X|)=HIE.Nh C =()*PaFv %$5')E[)*Pa()*G . C &(HIEjE[ C O ' C H H C *'Pa)*[5d-(! C 5)*Pa 5|[5d-G (') C FPh)*I(';EH(Pa j C .N gE[")*XRHPa C E[&(&()*&Z7E+FPh C FQ=' C HIE C ZN L%w'57E C Ke; KJ M C F Ke; e M C ;H\[5 C &(|=' C HIE C Z *a_)*XRHPa C Y7%_* PaXE[()NZN_Pa()* *(X[ E H7EF C jVFF .E C . N E[]5 C w)*'X;EHINT)E7E|k[ H\[© ;&( C (' C E[]P_GFl J1B P ? QI DKJ c(c(cNM ?H(Pa C F(&( C (' ¨g["X)* H"F E)* ';E C PhN* -)Nd-()gE["H(')**!E Pa g[G' 5H[5 C &( C E["*'XX.N* F"*_[5-(!)*X|)*H'*E C C H C *'Pa)* ||[5-G (') Y-G C &W*W)F C F~E[Q\7E!-)* R%E[] C F'E)*NT C F©F)* .-ZF©E[]X)* H]F E)* ';E C ZE[Y*\7E'jE[Y C F'E)Nh C ]X|)* GF

t ='.N_H\[5)EHIE)* Fv ¨OG'*HIE C

e; KJG U We; KJG _FIEHI)E .?"E[ E)E C * .E C )*'I ;k[ H\[F C "k[57E[" C F'E)N C X|)* GFt+1

PhN G(] (Z * (\[X)*(5 .DNQF E)* ';E C ¬E[ C G+ C F'E)N \7EG&( .-( CE[" C F'E)N\7E"X?)* GF

t C F .Eg[ E()N(

0:%<=: QHG;F;R @ RTP6QHFH@;AC@ JK

VYlPa C E C F!|<-( 5)EP H C PaX)*<-(% .EvEH\[ C ((&N < E dkj)l .EX)*wF'HIE C H*EγitZNQ Pa \7E C & C ; E C &YEH[ C ((&N]¬H(PaX|IE .E()()wNQ CC d-77E C & jE[_HIE .-Z

.E +)*w' )* 3 ;X? C F .E')* ¨g[ )**'.E 5)*P 3X)*GH*)* EGH\[5E H C F E[_ ;X? C F .E')*] C )*_&(<-() C F ZNu)*(';E C hg[*h)*(';E C ])*_FH * C )*'+=()¨E["F'EPa C g 3 ;X| C F .E')*gE[57g\E[ 5)*P +[ E()Nh C EHH(' C A **'PaF_E[57E[|[5-G (')E5)*'g * PaX+E7E 5H C & PaH[5 C *P Xg[]-7']

γi,t+1

FIE)*Pa C F©ZNT_ kj7D\&(!)E C F(P X)*GHIE ADC E[5)*\&( . Y C .NG*Fk[IE[)E[QHIE .-G .E g C F'HF©ZNE[ ;X? C F .E')*FEW C N)**'.Eh7h g[ _ _)*X)** C EFZN C FX? C F C W)E C F(P -)* R

dmit C F

dnit

k[ H\[\ E[ -7' @ .lE[)*" C Pa \7E . C ()g CC <-77E C DF)Ek () )*a .lE[)*)* C )**'.E XyX g[ X)*(5 DNa)*HI .-G C &_QF)Ek +X|(* .E .-Z.Na)*R7EFhE_5)*P ;X? C F \')*

Prob[dmit = 1] = am · rmit ·Kit and

Prob[dnit = 1] = an · rnit ·Kit,

Ke; U M

k[)*am

C Fan)* X?(* .E .-( X5)EPaIE)*

] 14W R"]5b; . . ..'r~.X0Azcpmqw_hnodmq!k#"q!qwa%qzu!Vp a%qs_v `!bVf2$~]!]1"sbVa1dmnoa%c$ abVd e"ndmq/c _dmq!qw_erVu!_ok#a%q!q _ $au!eVd e.`!bVanou|c#9q%'oqwaa 36572989+.:<;=>*?&XD'r~I&>*>@Ay~

7U


ADC E[*H C F\&(E[(';EH(Pa_E[F)Ekh)*FIE)*Pa C Fv g[ a F C ZNF)Edk C & )\ C F(Pa.NQY-'

γmit=)*(P E[gF E)* ';E C 1K=HX .\ kj &([ZEF M X)*GF'HIE C

H(EΩt(γ)

C E[] C F'E)NT7E Pat . 5)*P

i[5 C Pa .E7E . C F)Ek K

dmit = 1M ¬ C F

wNF)Ek C &_)E C F(Pa.NWQ-'γnit=)*(P_F E)* ';E C EH[ C (&( Hv(XX|()E' C .E

Ω+t (γ)

. 5)*Pi[5" C CC d-7E C F)Edk K

dnit = 1M VY" CC d-7E C & PaX. . ;X()* C &

C Ik EH\[ C ((&( j * %EH\[ C ((&( k[ H\[H'*T<kj)_H(EaE[5 C E[(*k[ H\[)*H')*)* C E.N '*F =()!X)EwF'H C & =()Q C CC d-7E C F)EkE[WFw'57EF E)* ';E C &( C )E7EFTZNdkj)* C &_H\[X?)* GFE["Pa C E["F E)* ';E C X)EwF'HIE C H*EwN_E[Y&()*dkgE[W)E7ER7E C j C <kIF&(

Lt

%V++R ZE[Y)**'.EjvE[YF)Edkj[5-(YE?"I-'5<\IFv ADC X?)* wF

t+ 15)*P

iX)*GF'HY7H(

γi,t+1;k[)*

γi,t+1 = minγit, γmit , γnit,Ke; K^ M

* E[ 5)*P X)*GF'Hk .E[E["?Yd-7 R.YEH\[ C ((&N( L ;X? C F .E')* C CC d-7E .-(uHIE .-G .DN )*u C .N? C 5H R .!E[,5)*P H C ;X|HI~H)\ C X)* =)*(P C CC d-7E C g[ C *')*F ZN~**'Pa C &WE[57" C CC d-7E .-(EH[ C (&NhH CC +? Pa \7EFh PaP_F R7E N( ADC EF .+ .j)*I-ZFWEQE[) 5)*Paj*E[57¨ C E[ 5)*jX|)* GF ZE[ CC d-7E C D C -G * . Z C F w C *'*w'5 C +X?)* GF w . )*I-Z7F~&()EF'5.N ?*hE[57 79E)Y*(PaQX|)* GFE[QX57E C X)*EHIE C - C *[ g[)* *Tj? C & Pa .\<EF~FX? C F! C E[ 5)*P* QVY E[ Pa .E7E . C F)Edk")* \ C=)*(P E[F E)* ';E C &#Y! & # 7 *"! X)*GF'HIE C EH\[ C ((&( ¨E[X)*(5 . .DN=()WR)*&(5)*P E| Pa \7EFT Y[ &([)E[5 C =()W*Ph 5)*P g[G' vE[Q ;X|HIEF? C E C CC d-77E C C H)**" .E["* E[ CC <-77E C & 5)*PFH)**

0:%<=: F? RTS D RTF D

g[ HX .\?EGH\hFIE)*Pa C +(';EX'; C F jE[w' C PaX?()\ C jE)\<\I&( HY-7)* R=()E[ 5)*P Y'E FX)*H R7E C GE[ HX .\¬EGH\W*[)* C wgH\[X?)* GF7 C C F'E)NZk FjH C \ C )E7E

δ X .EX?(* .E C K=Ph)*I*[5)* M E[ 5)*P [5lE C -( C .E

HX .\¬EGH\| g[ HX .\¬EGH\hlE[ C GX|)* GF +FIE)*Pa C FZNWE[ C -(EPa C w'57E C

Ki,t+1 = Iit

(

πit,qitQit

, Kit,λ0(N − Et)

#Zt

, δ

)

·Kit + (1− δ) ·Kit.

(^


g[a C -(EPa C "=' C HIE CIit(·)

&( .-(!&()*(*" C -ZEPa C !X?)!' C ."HX .\ A ]FX| C FX?(* .E .-(.NT C E[_X)* E

πitE[_)E7E j*(F~EX)*GF'HIF ' C .E qit

Qit

E[_ ;X|HIEFC IkH'E(Pa)* λ0(N−Et)

#Zt

w C FQE[+FX)*H R7E C )E7Eδ ADC -(EPa C FX? C F C &Z7E .-(.N

C E["* Kit

E[ 5)*P Y* )*F C -ZEPa C

IDit

"R)*&()Y=()"*'HH**=' 5)*Pa ';]FH)**] C 5)*P* A *[('F©? C EF©E[57

Iit Y C .N C -(EPa C X|)' C .YHX .\ g[w' vR)*&(5)*Pak

C ()*Ph Na C -(Pa()*YPa C INaE[5 C *Ph.-5)*Pa+ C *(.';\ C 'PQ?)* [IE[)5)*PH C C -Z P 'H\[~ .YF* )* FX| C F" C .E C C H RX?(** E . $5)*(P |<k C -(EPa C ?(' C FFuwN )* l C F©E[ 'XX?) |(' C FuFX? C F" C E[ C E)*")E7E+kj5)*P +X)* E X A X)* E)* X?E \ -Z5)*P C C H R¬X?(** E .+)*?I*E)¨E[5 C k .E[ C &Z7E .-(X)* E V C (&(('%E ACB P ?H K @dn U ZXv Ge @dnNM w C -(EPa C k .E[ C E[ C C H Rv P_ g gHH'R7EF

IFit=

δ + 3 · πit

Kitfor πit > 0

δ + πit

Kitfor πit ≤ 0.

Ke; M

)*(* C -(EPa C X?)' C .HX .\¬=() 5)*Pi C X?)* GF

t +E[ C &( .-Z C

Iit = max

0, minIDit, IFit

.

0:%<=: >0E D

$ )*PalPhN" ; .E[jPh7)EI=() kjY)** C %$ )* <E[jHX .\ZEGH\"PhN"*[)* C "|<kPa C PQ'P .I-Z C H*E)NQ=()X)*GF'HIE C K=Pa C P]'P <aH C *H M g[ H('F_*? C E)*X)*IEF C C H R)*E)* HIE C X g[_E[) )** C E[57 E[ X?)=()*Ph C H-)* R

Xit

?dk hH)* .E Hv-' A )*w' )*F©E[57Y C E[]*[())*' C v 5)*P*[('F|"YE_Hd-()7gg .Ej-)* RYX)*GF'HIE C H(E

γit C HE[ H)* .E H

-'X|)=()*Ph C H +&( .-( C wN −(ρ+ δ + rmit + rnit) YE[)k *;E[ )E7E+)*IE') C

C HX .\l)* EG_dk k[ H\[T gH'*F©ZN ;X? C F .E')*Y[5-G C &a| C Ewadk" ADC E[aPaGFX)** C EF [)*E[)*W)*hFF .E C H )*H'Pa\ C H!k[ H\[ PhN~H'*]= #Ce `!bVa,36572989+.: ;=>*?&X0Azfl_Vnoap`!bVa p d fla%qD_v u!_ q!q/d e0$a%q`!flae `1dmqDaa` "cp`!_

δd vfhcu!a#`Iqwb"cu!a7ce"n

rVu!_ V`|q`!ae"nj`!_#scu|nVqau!_D' d ~wa~d ej`!bVaIp d fld `!d e.lkcqwaD_vTrtauwvxa%ky`/k#_flrta#`!d `!d _ej`!bVa1kcrVd `|cp q`!_Vk!hu!afhcd e"qk#_e"q`|ce `%~]=#aa ,14W R"]5b; . . ..'r~DG*Ay~


C ; . V 5)*PPhN_[5-(Y5Fh'H\ <-()j! C &()%E PaX?)* wFW C Fh)E)*.N EI?5 .EX)*GF'HF©&(GwF OG C H"E[ )* O HIEF~ C a)*F'H\ . C %X)* E |E[ ; .YH C F .E C WHd-()*F ZNE[~X|)=()*Ph C H©Pa*')*

Xit

A W* C H'FF C \[ 5)* ; .H C F .E C ?IH'* F* )*F~ C -(EPa C C &Z7E .-Z.N";¬HIEF~ZNT5F©E C F ?E[G' E[gHX .\GEGH\QPhN]*[)* C | V=')E[)H'*? ; .%)**'.E=)*(P X)* \ DN( A |E[X)*GF'HIE C H(Eg)*EwQ[ &([hH(P_X5)*FhE]E[Y)**)-77E C X)* HYvE[YH C *'Pa)* 55)*P[5¨EQ ; .jE[YPh)*(I G * G . C E[ C &!)E' C

ϕt ≤ Pit < cit g[*(YH C F .E C

E[57Pit < cit

C *' <aH C =()Q ; . |H'*E[5)*P H C .k+dNG]E)N E~*j .EX)*GF'HIE+ C E[*[()g)*' C 7

ϕt ≥ Pit = γit %g[w' |5)*P[5jEQ ; .+ .

Pit < γit; *

.-7)* RX)*GF'HIE C H(EY)* C H<-()*FTZNWE["X)* H

g[ C 'P |)Q ; .E C & 5)*PaQPhNu-)N =)*(P X|)* GF E~X?)* wFv ~g[X)*(X|()E C ; .E C & 5)*PavE+E[%E\ C 'P |)l715)*Pa

Zt

Pa*')*F"ZNE[ K= C F(&( C (' M -)* Rζtk[ H\[ .E*. _FIE)*Pa C C E["H C *'Pa)* 5)**)-7E C X)E .H

ϕt+1

A 5)*P &(G 5 C w)*'X; ¨ . ; .EQE[Ph)*I ¨ C F (* .EQHX .\jEwH| A E H' E(Pa)*][5-(hET\)Q*)*H\[ C &T=)*(P C Ik" © C HE[ C GQX)* Hak[ H\[ E[IN k HHX;a _ C N X)* H?dkE[ ) )**)-7E C X)* Hj C F PhNG?R)*&()]E[5 C E[ C X)*I-G ('*.NX5 Fv ADC E[]*[())*' C |E[]X)*(X?()E C %X?E C E RlH C *'Pa)*Y C H)** ADC HI C *w' C H GE[Y)*Ph C C & 5)*Pa¨H C ;X?HIgPa()*)E C F(Pa.NQPh7EH[FhH'E(Pa)* VFF \ . C N |E[INT[5-(QE[]H[5 C HQ C H)** C &hE[ )H'E(Pa)5*¬k[ H\[~Ph=')E[) ;X5 C * C X?(**

E+E[57* C HgE[gPaGF EGH\[5E HZE[g*'HH*jv 5)*PFX| C FE"*(Pag GE C C .E!'H\u C Dk+©F Z;¬)* C !kgNG .E[(';Q C N Pa \7E . C ()] CC d-7E C F)Ek E[5)*P gEH\[ C ((&N?H(PaI(';EF57EFT79E)Qk[ " C F C E[! C & )*' C E[5)*PPhN ; . gg[]*H C F©)E C F(P H(PaX? C C 7)E]5)*P E OG C HQ5)*P H C C .N=()*P ;X?HI\7E C glE[ w'5 C E .DNhFPh C FFGK= C k[ H\[ .E+X)*wF'HIE C FH * C .g5*F M E[)*©X?(** T\7EWH C GHH') 3$ )* +E[ C 'PQ?)h"H'E(Pa)* Eh HIE.N¥E[w'5 C E .DN¥X)*wF'HF W *H C F gE[ 5)*PbE [5h*(PaT' C .EaI9Wd-() W E[ )*F.N jE[)*)* Pa()* H'E(Pa)*E[5 C X)*GF'HIE"X)*GF'HFv g[5)*! C F~E[ E[ )*F~\7E_F C H'*© C N X)*(Pa j7aa=) \[ 5)*Pa C E[H C E)E)N ¨\[*H C F\7E F5 C &()*(' .¨GHH')*)* C &d-()" C &()*w' C Ha¨X?)* wF ]g[ ?H'* E[ 5)*P[5F X)*GF'HF EGH\~k[ H\[ .!F F C ]*H(PaXIE.N( hVY] .! ]**'PaF E[57!E[&(GGF)*QX?)* *[5?E[5)*P C H')*H(E X)*GF'HIE C '; [5 C C H(Pa!=()Y .

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[ &([v %l7E) C GPh)*Ij*[5)*+)*)*R7E .-Z.NQ\Y C F 5)*Paj)*Pa()*H C H C E)E7EFv VY+=')E[)+DNG FWHIE+*["FF+E[ NGPaPaIE)Nh/5)*P D* YF E)* ';E C w\[X?) * E C H© X)*wF'HIE C EH\[ C w' C F +E[)*I=()*gH(E C FX)* \ E . + C FF Z;¬)* C H C CC d-77E C HX5 .E . A "&(wk .E[('; ENG C & C PaX )* HlH C (Pa HYE[57 5)*Pa")*Q[IE)*(&( C (' k[ H\[[5 [<kjI-() C "NZI]| C C E&()E7EFu C EPa(!P_ H)*GH C (Pa .HQE[()* ADC EF E[ C E C ¬E[)*X)** C \7E .-( 5)*P %E F(Pa C 7E C & Qg[*X?H R| **' !$#$& & 4 ,a&! 45*6&"78 @n(n ( h K @VM H C \ C ]X?w(%+X5X?)*!H C H) C C &5)*P[IE)*(&( C .DN( ADC E[*!H C E)* ';E C g .g*PagEa|!HHX;EF© DNG FHIE[57jE[YF Z;¬)* C H ;=()¨ C \ C H; C X)* Eg C FW CC <-77E .-ZYHIE .-G .DN ;)*YX|)** E C + CE["k+NE[57X)* EF C H C -()*&(!Eh_* C &(. -7'! C FT CC <-77E C )*]';EwH() )*R7EFv %$5')E[)*Pa()*w=()Ph C N_ C F'E)* ¨ .¨ ¨*[<k C E[57¨E[ 5)*P D* F \)* ';E C Yw'5()7* Pa )gEh*IkjFuF E)* ';E C ?*'H\[ E[ `)*IEW()E[Q(&7C ()*PhF E)* ';E C FIRT?BV?? K @dn nNM F*H)* ? ! NG IF HIE!E[57!E[)*)*X?)** E C jF Z;¬)* C Hj C 5)*Pa ZX)* Ej C F_E[57E[F Z;¬)* C H¨ C X)* \ .DNQ)*Ph C .N C F'HIF~ZN5)*P D*X?H 5H!H\[5)EHIE)* E H g[*]E(X HY)*Q C .NG*FT C FI\ H C H) C C &_E["F57\ &( C )E7EFwNWE["* PQ'R7E . C PaGF

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jI=()*_W* P 'R<E . C PaGFH C |_)*' C vE[ X5)EPaIE)Y-7'" C F~E[ C .E l-7'*(Pa"E[ -)* Rg[5d-("Ea|!*X?H 5F 5=() C \ C H5E[ C 'PQ?) 5)*Pa E[ C .E R7+HX .\EwH C FX|( HIN X5)EPaIE)* ACB P ?H K @dn U M *(.-Z_E[ _\* ZN\)E C &\[hPaGFk .E[ E[h C E)E C HW C 5)*P C E\[hPh)*I ©V9E)Qk[ E[) 5)*Pag C E)gE["Ph)*IE[w'Phw C & .I-((.-( ADC E["P_GFvH C E)*'HIEF©[)*E[ X)*wHF')*QH CC Y|QXX F|H'*Q*I-()E/5)*PaY)* C H*E)NEWdk =()Y

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U


C C DF&( C )E7E+X)* HjF E)* ';E C lg[)*I=()*wYX)*wH*%* Pa )vE )J IF K J c(c(cNM[5? C XX F]EH )E7EE[+* PQ'R7E . C PaGF g[ X)*wHF')*+kj()*w=(.dk g[QE .P 'R7E . C YF .-G FF© C Ea kjWX5)E lH )E7E"E[QPawF ¬ *[() ?-()** CE[ PaGF )*' C !g[ Ph ()YX5)E vk[ H\[ HH(' C =()YE[ PawFF;N C Pa H )* ;H'FF C Pa.NE[j CC d-7E C X)*GH*% C F]HX .\wHH'PQ'R7E C )*ZN 5)*P D* F E)* ';E C g C FX)* H F E)* ';E C g)*"(;\ C Fv %V9E)e c X?)* GF 5 C w' .)E .'P j'*'5.N_)*H[Fv g[Y-7'+(;\ C Fh C E[RjX?)* wF)*\( C j C .E R75-7'=()+E["H(PaXIE PaGFv)*' C ADC ()*F)+E_ C .NG*E[ PaX5HI+F Z;¬)* C *)*H\[ C E C * .E + C E[ I-Z(.';\ . C lE[Ph)*( E[W C .N X5)EPaIE)*]E[57_7)Ea-)* F )*hE[W*)*H\[ C E C * .E

λ0 C F

λ1

)*λ0 !E[W*)*H[ C E C * . N X?E C E R¨H C *'Pa)* % * E[(*WH C *'Pa)*]k[

C E C F_E]X')*H\[5*E[&(GGF w';¨k[] .E[)¨[5-( C ¨=(' C FW"*'XX )*!)¨()%k[F C 7"H')*)* C E.N©[5-(aW*'XX )|H'* E[ )Y=()*Pa)*'XX .)[5 &( C 5 C w)*'X; λ1)* O HIEQE[W*)*H\[ C E C * .DN HIE'5jH'E(Pa)* % * lE[(*WH C *'Pa)*Qk[~)*

H')*)* C E.NhPh7EH\[FWE_Q*'XX ) VYg .+FG C gPh* C * E )*' C E[ P_GF?=()gX?(** _H(P C 7E C +E[_Dk+X5)EPaIE)* =(')"H*Q)*aH\[(* C K=*aaU @?dk M $5()lH\[QH(PQ C 7E C

λ0 C F

λ1 C ¨*I5 C .E -7' l&( C )E7EFv %LH\[

H C 5&(')E7E C *)*H\[©H(EE[ C )*' C @dc(c E Pagk .E[-)NG C &a)E C F(P C 'P |)* YX? C F C & C E[ C .E j-7'YE[)E C F(P C 'PQ?)_&( C )E7E() jE[)**'.E_k -)NhI-( C =()¨E[EPa C .E |X57)\7PaIE)+ C FW-)* R-.' * C &]E[EPaY C .E R7-'3K= ;HX;"=()YE[ )E C FP C 'P |)* M C *')*"E[ H(PaX5)E . DNE[ F Z;¬)* C PaGFv)*' C C F(P C 'PQ?)*gXRdNW )*(G=()g C \ C H C FIE)*Pa C C &]E[-' C Pa \7E . C () CC d-77E C ()gE[ C 'PQ?) C E)E C \ g¨N ; C &_E[! C .E ¬-'"E[")E C F(P C 'PQ?)&( C )E7E() H\[T)*' C H C ?")*X)*GF'HFv E E[57" C E[_X)** C \7E C F E C HIE C PhF ?IDkj C * C &( )*' C k[ H\[ )**(PaIE Pa]'*F7 PaX C F E[-()E&( @dc(c )*' C Qk .E[ F C E H¨X5)EPaE)Y-''; F Z;¬)* C )E C F(P C 'P |)* "g[_-()E&(")*]HH'R7EF©?H'*QE[)**'.E_* C &(W)*' C _FX? C F¥ C E[H\[( HE[)E C F(P C 'PQ?)*a C F &( C )E7EF Z;¬)* C [ E()* ©Vl-Z)E& C &uTR)*&( C 'PQ?)])*' C ]\QE[ ]X[ C (Pa C C C EHH(' C " C F~ C *')*E[57YE[](';EH(Pa](*)-(Fu =)*]=)*(P )E C F(P ;¬HIE V C (&(('E ACB P ?H K @dn U M @dc(c X|)* GFH()*)**X? C F©EJ(^ N()* Yg[ Y w' .E]h C &

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*X5 C E PaYE_EI)*-(! C )E 5H R?H C (P]N k[)*" C .NhE[ F )*HI C -G )* C Pa C E[ 5)*PaH\[5 C &( 5';E["&( C )E*ID'X)*Ph C +E["EPa OG C HE[T* PQ'R7E . C _&( C )E7EF &()*7akj.E[ F57\ .h C .E[)aX?(** C ()C H*E)N E~)*X?()aË[FI\ ADC EF Ë[(*W-)* R C F )*R7E C *[ XQ)*X)** C EF©k[ H\[~)*!%Ph () C E)*=()E[ E'F;N( g[]X)** C \7E C )*E)* HIEFEgE[%=(')F Z;¬)* C lH C ER7E C v;*)*H\[]H(El*[dk C C %U @ dk *)*H\[]H*EE C FhE]F)* .-(E[H C (PQN Edkg)*FjHI(PaX?IE .E .-(';\HI(Pa ; * G-()E&(YX)* Hj*[('FE C FuEE[ H(PaX?IE .E .-(QX)* H ?H'*_k .E[udk *)*H[ H(E"H C *'Pa)*!)*_Pa(X?)=HIE.N© C =()*PaF[K=H* AM vg[ PaF 'P H*_)*X)** C E"E[ * .E'57E C k[)*_*(PaH C *'Pa)*])* kj D C =()PaFu C F E[)*])* C K=H* A*AM g[aH*aj[ &([u*)*H\[H(E")*X)** C E"E[QE C F C HIN©E<k+)*F Pa C (X?(.NX)* H ?H'* E[ H C *'Pa)*")*5F.N_ C =()*PaFh C FWPhN_?Y ;X( .EFhZN_E[Y*'XX )*ËQ!H)\ C GE C )K=H* AA*AM ADC ()*F)+E &( C )E7E"QH C E)E 5Q)*' C k .E[[ &([

λ0 C F<k

λ1k+X|)=()*PaFGK=H*

A M A k j?FPa C E)E7EF ?dkE[57λ1XRNGa~Pa)EW PaX?()\ C Q)*(WE[5 C

λ0 C H[5)EHIE)* C &TE[WPh)*I E)*'HIE')*%k[ H[ k+ X)*F HIEF ZN E J1H P ?BV?B C F ? FIBDB K @dn ( M

"U @ ïj C ER7E C +`)EPaIE)*`)EPaIE)*

λ0 λ1i+*i+* A c U c KJi+* A*A c c Ui+* A*AA c c i+* A c c KJ

g[¨ C .N X5)EPaIE)*v\[5<)*%-)* F!|I kj C E[%=(')lH*)*%E[*)*H[] C E C * .E a

λ0 C F

λ1 g[5* HY F"=()E[Y&()*('X C &]lH*g ¨5*F C E[YH C (Pa HE[()N

=(dk C & E J1H P ?BV?B C F ? FIBDB K @dn ( M wE[57λ1 jE[ FH * .-( X5)EPaIE)j=()

FIE)*Pa C C &QE["Ph)*(IE)*'HIE')* j$5()+E["F Z;¬)* C H"?IDk+ C E["*)*H\[T C E C * .E !X?E C E RYH C *'Pa)* C F HIE'5YH'E(Pa)*\ C F5)*FH*

λ0 − λ1 = 0.2

H[E C ¨V =(')E[H*" +H C *E)*'HIEFE C F(';g=()¨k[57;¬HIEλ0 C F

λ1HH(' C

ADC E[ H*5E[!*)*H\[T C E C * . NX?E C E RH C *'Pa)*w'5E["[ &([-'"[/aflaf2$ aus`!b"c`Dc bVd bgqwa%cu|k|b d e `!ae"qwd ì d e"nodmkc`!a%qsp _ qwa%cu|k|bk#_ q`|q/ce"n $dmk#a $au|q!cV~

(

U e; OG PQ'R7* C *'.E A RF P ACJ1B

E[+*\ C F57)EF H* Kλ0 = 0.8

M C F]\[+*)*H\[_ C E C * .DN]?HIE'5;H'E(Pa)*%w'5E[dk+Y-']'*Fu C E[Q\ C F5)*F~H*3K

λ1 = 0.2M g[ .Pa C ?E[57 .Y YX?(**

E©F Z;¬)* C E R7E_k[IE[) H)\ C (*)-(F X[ C (P_ C C !Ph C N ";¬HIEF wNuE[*)*H[WHIE .-G .E %¬E[X?E C E R5H C *'Pa)*

λ0G()%E[*)*H\[H\ -G .E ¬E[HIE'5

H'E(Pa)* λ1

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>( 38 4 ,980:+ 94,

ADC E[ ]*HIE C E[WF57\gE[W* PQ'R7E . C )*hX)** C EFv uL ;XR C 7E C ]+ NGX HX57*E) C )*&( .-( C C FWE[F57\ )*-G *'5 FW C 5&(')* C F*'PaPh)* FW C \ g[©X)** C \7E C aF .-G FF C E E[)*©X5)E 3`) @ H C \ C 5)*P D*X?H 5HTF57\; `) J )*I=)*EhX)* H!F E)* ';E C jV C C .NG* E[!Ph)*IYE)*'HIE')*] &( .-( C CX5)YeG ADC OGHIE C U U ;E[")**'.E)*"*'PaPh)* IFv g[[ E()N C C F'E)N H\[5)EHIE)* F¥ZN E[FI-((XPa C aE[ 5)*Pa E[X)* H ? C FE[!Ph)*I\)*'HIE')* ¨g[!)**'.EFX? C FT C \[" GE C Y*)*H[H(E $ )*PaY)*]H\[5)EHIE)* F~ZNLK9E[QFI-((XPa C M E[ )YHX .\lEGH\ v(';EX'; vX)* HIC 'PQ?I)H'E(Pa)* 5X)* 5X?)=()*Ph C H;E[ ) 3X?( HIN C F*'HH* ¬ C FE[ ) C -(EPa C S )*IE)*'HIE')*+ l)* O HIEF ZN!F Z;¬)* C Pa*')*lE[ C 'PQ?))5)*Pa E[]=)*w' C HIN© C E)* C F~ ; .E ?E[Q .9IE P_! 5)*Pa ?E[QH C H C E)E7E C 5)*Pa C Fa \ N! C F QE[57*[dk%E[g C E C * .DN]¬H(PaX|IE .E C )*&Z)*F*%?E[g GE C H C H C E)E7E C g[WF57\T)*aX)** C EF =()"E[a=(')!H C ER7E C !

λ0 C F

λ1Pa C E C F |<-(

A C H*E)N ?E["E Pa *)* [5d-(]*a? C F .-G FF C E E[)*!X[5*YE["Ph)*(IX)*GH* "g[5)* X[5*Q Y C Q()* C \7E C K9E[Q)*.NPh)*IX[5* M ¬E[Q*H C F YE[_X[5* ¨H C *( F57E C C FuE7E R7E C v C F~E[ R C )*I=)* EWE[ X[5*_E["FH C E[" C F'E)N( g[hPh ()* .DN©jE[aF57\X)** C EF )*aPa C h©-(( F )E C F(P;¬HIE =()"H\[H(PQ C 7E C |*)*H[ H(E @dc(c )*' C [5-(g| C X|)=()*PaFv $5() C \ C HE[g-()E&(HX .\EwH YHH'R7EF©YE[QP_ C %E[QHX .\EwHw¨ 5)*Pa ; E C &h C

Z


X?)* GFt=() @dc(c )*' C ADC E[¨&()EX[ HZX)** C \7E C <E[jPa C '*'5..N"H(PaX5)*F

EE[D?I*%X)EHIE H ( * 7=()H\[_X?)* wFQE[+-7'%|E[+? 5)*P C \[gHH()*F C &X?)* GF )*hX*EF K=Ph ; PQ'P M hVFF .E C . N©EE[hPa C C F E[aPh ; P 'P E[Pa C P]'P C FE["\ C F5)*FTFI-G R7E C )*"&( .-( C ¨g[)*I=()*| .H C * .NW?"-()* 5FE[57 .E[('&([E[] C .E H C F .E C =()5)*Pa)*] F C E H 5E[INk lF Z;¬) C Pa C N)**X?HIEW79E) *(PaE Pa[5_X5**F + * E[IN¥)*?H(Pa C &u[IE)*(&( C I(' g[F&()*![IE)*(&( C .DN g)*X)** C EFTZNE["\ C F5)*FFI-G R7E C

:0:/9 E I QHGJI6G;P DR+I6ECS DECP1S

ADC E[ %*'*HIE C E[gH[5)EHIE)* E H+5)*Pa%)*gE'F Fv %$ )*% C F_Pa(% PaX?()\ C E["FI-Z(XP_ C HX .\vEwHw C .NG*Fv g[ C H'FgX)** C E C &aE[!-()E&(HX .\EGH\ C F" .E¬-)* R . N E[%&()*<kgE[")E7EGHX .\EGH\w C E[% C F'E)N C F C .N <E[j&()*<kgE[])E7EHH()*F C &EF Z;¬)* C 5)*P * %OGH C F (E[jFI-((XPa C C -(EPa C g jF*H)* ?Fv g[ )*F 7*E C E C +&( .-( C E]E[FI-ZXPa C glX)* Eg C FX?)=()*Ph C H% C F =(')E[ E ;X? C F .E')*_ C F E[ )];¬HIE C Pa \7E . C C F CC d-7E C `( C /-(jH C H) C E[¨FI-Z(XPa C E[¨X)*GF'HIE C H(E $ C N dE[)*R7E C *[ X!?IDk+ C E[+w'5 C E .DN]*'XX IF_ C F]E[ C 'PQ?)|H'E(Pa)* C .NG*Fv

]:)694d:5¡

g[+ C .NG* 5HX .\ 5)**[dkE[575)*Pa)*¨R)*&()l C -Z)E&(7=()Pa()*X?E C E RH C *'Pa)*+ C E)¨E[YPh)*(I %j* F ; .¬E[Y*)*H[W C E C * .DN_vE[HIE'5?H'E(Pa)* [ &([ 5)*Pa%)*gPa()*j[IE)*(&( C ('%E[5 C .5E[ *)*H\[a C E C * .DN] <k" ij C H) C C &E[&()*dkgE[!15)*Pa < .H C ?(*)-(F!E[57E[&()*dkgE[!)E7El)* C &Z7E .-(.NH()*)*R7EFk .E[E[ 5)*P* 5 * *Ph 5)*Pag&()*dk E)+E[5 C R)*&( 5)*Pa ADC $ &(')*U @ +E[T*( F C *[dkWE[TFI-((XPa C W E[©-Z)E&(THX .\EwH 5)*Pa K=Pa CM =()©E[ F Z;¬)* C *)*H[ C E C * .E K=H* A A M "g[ F5*[F C !F*H)* ?aE[hPa C P]'P C F Ph ; PQ'P HX .\%EGH\wQ(*)-ZF C H\[ X|)* GFK=Pa C 7Ph M ag[hF*EF C )EIX)EIE C ]E[_-)* R<\ . C Pa C & 5)*Pa! C E)*Pa"jE[\ C F5)*FFI-G R7E C K=\F M ij C H) C C &QE[ 5)*+E[)* H* .+H C | C EFWE[57+ C E[ 5)*+Dk+QPh)*(I+X[5*E[)*a " C C H)**a C E[a-()E&(_HX .\EGH\ C F C E[ E[ )*FuPh)*I!X[5*a

(


0 10 20 30 40 50 60 70 80 90 1000

50

100

150

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

λ0=0.8, λ

1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &')EU @ %Vl-Z)E&Qi+X .\Ow\wH\

n


FH)** gg[] C H)**] C FE[!FH)**]E[]-Z)E&("HX .\EGH\)*!R)*&()+=()[ &([W*)*H\[ C \ C E \ . g[Pa C E[ -()E&(HX .\|EGH\a +*Q)*&()¨=()¨[ &([*)*H[ C E C * .E C Pa.N GH* A K ^ n U n J( M H* A*A KZG c ^ cNM H* AA*A K (JG K^(^ZJ M Vg"E[_ C F ¨E[a)*' C K

t = 100M lE[a-Z)E&(_HX .\EGH\wQ)* -()Nu* Pa ) C

E[)*QH*H* A K ^(^G Uw7U @VM |H* AA K ^(G c;@ (J M C FTH* A*A*A K ^; K^( @VM ADC FF .E C E[][ &([)*)*H\[© C E C * .E HH(' C Y=()R)*&()\ C F5)*F©FI-G R7E C C E[]H* A A*A*A g[ =(')E[Xgt;¬)*g*(Pa C * &([wE+ C EQE[ F Z;¬)* C ;¬HIE

λ0 C F

λ1 A *[dk

E[57!E[a)EIE' \!H C H) C C &E[hd-()E&(aHX .\EwHuFX| C F E)* C &(.N~ Cλ0 g[

Pa C gE[d-()E&(WHX .\¨EGH\w C H* A n c (eZ^G ~V+QE[W C F E[W)*' C .]Pa(' C E"E©Z^G e(^(; Wg[h\ C F5)*F FI-G R7E C ")*R7E .-ZI.N~dk. ( E[a\ C F5)*FFI-G R7E C C H* A k[)*E[Ph ; Paj C X5)E H'R)¬*[dk +* &([ZE.NR)*&()¬-7)* R DNE[5 C C H* A g[h\ C F5)*F FI-G R7E C +H* A H)*.N~* E[5 C E[(*ajE[H* A*A C F AA*A |g[! C H)**! C E[!d-()E&(!HX .\vEGH\F')* C &aX[5* A C F AA Pa(YR)*&("Y C H* A*A C F A*A*A | * | Pa()*!F E C HIE[5 C C H* A ¬OG C H"E[FH)**! C X[5* A*A*A +-()N*dk 57gE[ C FE["d-()E&( HX .\¬EGH\WH* A E["R)*&(?=(')H* g[&( C )E+X57*E) C E[FI-((XPa C _gE[-Z)E&(H7X .\jEGH\ Q* Pa )! C¨=(') H* j';_ . F Z;¬)*Qk .E[ )**X|HIaE©\[I-( C F -7)* R DN( g[*)*H\[ C E C * .E I

λ0 C F

λ1H'*QF Z;¬)* C ;¬HIE ij(PaX5)* C &aH* A K

λ0 = 0.4Wλ1 = 0.2

Mk .E[ H* A K

λ0 = 0.8Wλ1 = 0.2

M Z .%H C | C EF E[57%k .E[_[ &([)*)*H\[a C E C * . NX?E C E RH C *'Pa)*

λ0?E[ -ZI)\7&(QHX .\EwH C H)** C FTE[Q C H)**Q

E[a-()E&(_HX .\EwH©F')* C &WE[5)*"DkjPh)*I"X[5*! Pa()* F E C HIE[5 C C H* A*A C F A*AA |k[)*\[!*(X?"E[!FH)**Q C H* A Pa(Y&( C E! C H* A lg[a*)*H[ C E C * .DN~H\'57H'E(Pa)*

λ1 C O ' C H!E[a\ C F5)*F

FI-G R7E C gg[][ &([)E[ )*)*H[~HIE .-G .DN 5E[]Pa()*"F .-Z)*&( C HQ?IDkj C 5)*PaH C?"(*)-(Fv jI=()*hH C HI'* C Q|(';!E[hPh)*I]E)*'HIE')*W)*aF)Edk C *(PaaH(PaPa C E! C E[;¬HIE]+*)*H\[ C E C * .E "*[('F ?aPhF hV+!E[ 5)*]&(R C Hl[ &([.NuHIE .-(_X?7E C E RvH C *'Pa)*-(()R)*&( 5)*Pagk .E[T_E C F C HINEdkg)*FY_' C .=()*P F \)* ';E C 5)*Pa .

λ1 _dk" g[ _H('F ? ;XR C F¥ZN E[)E C F(P ;¬Hh

λ0 ¥ &([

HIE .-G .DN©wN~X?E C E RH C *'Pa)*"Pa C E[57!H\[ 5)*PH C ;X?HI]Ph C N~H'E(Pa)*)*&Z)*F*+vE[X)* HY .jt;¬)* &([W*)*H\[HIE .-G .E ¨lHIE'5¬H'E(Pa)*

λ1;[5g

n(c


H C \)E)NW;¬HI VY [ &([λ1\ C Fg=()+X)* H"7*E C \ -Z H'E(Pa)* 5)*Pa+k[ H\[t;¬)

dk X)* H_)* **Fuk .E[uPh C N©H'E(Pa)* k .EH\[ C &=)*(P*'XX )*Yk .E[u[ &([)X)* H K9k .E[_\[X)*(*X?HIjE[57¨E[INa)*Ph C dNw M VY+!)**'. G*(Pa*'HH*=' 5)*Pa&()*<k R)*&(Q C F©Ph C NE[)*)*Ph C )*R7E .-Z.N*Ph 5k[57 Y C F H7EF©ZN~h[ &([)\ C F5)*FFI-G R7E C C H* A*A C F A*A*A E[5 C C H* A C F A k .E[_dkj)

λ1

*'P,'X g .WH C ? C EFE[57hE[©Ph)*IWE)*'HIE')*TE[57WPhN¥Pa)*&(T C E[ * P '7E . C PaGFk %?aF*H)* ?F ZN F .-Z)** .DNu 5)*P * I = F hIQ 7K @dn(n e M*'&(&(!E[57"E[a)** C k[ZNu*Ph 5)*Pa"H C H7D ; !k .E[uR)*&(5)*Pa" C E[aEPaPh)*(! E[57"*Ph 5)*Pa" ;[ .![ &([) X)*GF'HIE C O ; . .DNTE[5 C R)*&( 5)*Pa g[IN©*a)*X?()E[57E[ [wNGX|E[* *'\ C F©ZNPaX )* HvF57\_=()E[]X|)* GF@dn c @dn c C C E[)E'F;N( ADC $ &')E U @ C .NF57\_H C HI) C C &aE[!-Z)E&("HX .\vEGH\)*"*[<k C jg[!\ C F5)*F F-G R7E C C F H7E"E[57 C 5)*PaQ)*hgE[WEPah* ©g[('&([ *\)E C &k .E[W* Pa 7)%-' ;H\[5)*PFI-((X+F E C HIE .-(.N( [ C C F C &Q'Xhk .E[hF Z;¬)* C * lE[5)*Pa"PQ'"&()*<k7!F Z;¬)* C !)E7E _g[aw'E C )* * k[\[I)!E[)*_ ~&( C )EgX57*E) C k[ H[ E[&()*dkgE[ X)*GH*aE[5)*Pa =(.dk V C )*.N E'F;NH C H) C C & 5)*Pa 5&()*<kgE[ A H/F P K @dn e @VM h"=()*PQ'R7EFWE[![ZNGX?E[* | C dk C )E7 lk`%)*(X|()E C 7E )*dkgE[ (E[57 5)*Pa%&()*<k)*&Z)*F*¬E[ .)* * | 5)*P g* " g&( .-( C ZN

kit = α + βi · ki,t−1 + εit,

k[)*kit E[Q(&hE Q 5)*P

i7E Pa

tPa*')*F~ZNE[QHX .\EGH\

α E[

C F'E)NZk F&)EdkgE[ )E7E 5)*Pa ¨ C Fε _ C F C E H N C F¥ C FX| C F C E.N

)E C F(P -7)* R A E[]HG<aH C ¨';EGH()*)*R7E C βi = 1∀ i E[ C " .)\< Ylk[(F ¬ * 5E[Q&()*dkgE[©)E7E] 5)*Pa=(dkYa)E C F(P kg K9E[Q&()*dkgE[©X)*GH*[5

' C .)*G M [IE[)g!-)* R7=(dkj!)E C F(Pk+ j'*'5.N EEFwNhXX.NG C &!E[ Y HINZ$5')YE!=()"' C .")*GE g[ C '%[ZNGX?E[* !

H0 : βi = 1∀ i hlE"=() E[X)** C Haj' C .")*wE C ' C .-7)* R7E]E PaQ*)* "F57\ , RTRT?HUK @dn M C F =-A 1? f ^ u!a%k#ae`1qwVu$ai_e aflrVd u!dmkcp ce"n`!bVa_u!a#`!dmkcp "e"nod e. qDd eVd `!dmc`!a%n $i 57LI:JR@8N;=>*.#Azdmqd $ae $i

H \98J8F1 2 ;=>*>0O&Ay~ _u9noa#`|cd pmq%'Vqwaa1a~("~ :9+.+.2F+ ;=>*>*.'rVr~IG&Y*@Ay~

n;@


C F , RTRT?H K @dn nNM H C * F)*Ft\7E E HY()*F C )NT*w'5)*")*&()*** C A

E[©' C F)*.NG C & F57\<D&( C )E7E C & X)*wH* h C E&()E7EF K= * j )E C F(Pbk+ M +E[t\7E E Hj[5d-( C C D\ C F5)*FF E)* ';E C , RTRT?HLK @dn M X)** C Eg*HIEFH)* .E H

-'¨=()E[E %QX|)=()*PE[Y' C .j)*GË ; C .N E[(* 5)*Paj)*Y*HIEFW=)*(PE[Q)*X H7E C Y C F~X5)EPaIE)H C ER7E C k[ H\[~[5-(Q ; EFu C E[QPh)*IY=()E[Qk[(QE Pa "g[ ?H'* E[IN~X)*d-G F Ph C NT(*)-7E C " C Fu .H CC "?**'PaFaE[57Ë[)E C F(Pk+Q?[5-G (')¨FX| C F+ C E[ C &E[al 5)*P .=IE P_ U KJ *'PaPh)* +E[")**'.EE[ E=()g' C .)*GE

U KJG C F(P kg7hj[5d-G ()g$ )*Pa )*dkgE[ 7E

ab DF < −2.61 DF < −1.95 DF < −1.61 \c

i+*i+* A c c ( n c @dn Je c KJ n(n @ (Zi+* A*A c c (e(e c KJZ7U c UwJe @ ZJi+* A*A*A c KJ c(c c UwJe c c K^(Z eUZei+* A c c c ZJ c @dn(c(c @ Z(J

aDFq`|ce"nVq1vx_uS`!bVa Ddmk !ai@ Vp p au1`|aq` q`|c`!dmq`!dmkhVe"noauS`!bVa

H0 : β = 1~ "sbVa k#u!d `!dmkcp

$cp Va%q =o~ Y.*'@ ~ >@G 'oce"n ~ Y.1k#_u!u!a%qwrt_e"nh`!_hqwd eVd tkce"k#a1p a%$apmq/c`S>*> '.>@G '"ce"n > .vx_u cg`!a%q` u!a%u!a%q!qwd _e /d `!bV_o`lk#_e"q`|ce ` ce"n:`!u!ae"nN~# `7dmq7rVu!a%qwVfla%n:vx_u`!bVaqwd fVpmc`!a%nnVc`|c7`|bVc`/`!bVa u!_ s`!b_vc "u!f no_a%qseV_`9k#_e `|cd egcei nou!d vY`9_us`!u!ae"nN~b"sbVa eVf2$ au|qjd e `!bVa "u|q`j`!bVu!aa)ky_pmofle"q cu!a `!bVa rVu!_rt_uw`!dm_eVqh_v "u!fhq /d `!b5c-`!a%q`q`|c`!dmq`|dmk$tap _ 5`!bVak#u!d `!dmkcp9$cp Va~

c^9Vf-$tau1_v`!_`|cpT`!d flalqwau!d a%qIk#_e"qwdmnoau!a%nvx_uD`!bVa VeVd `Su!__`D`!a%q`%~ "sbVdmqDdmq1kcpmk#Vpmc`!a%n cq

∑100

j=1

∑150

i=1 I100fji' /bVau!a

fjidmq`!bVaIeVf-$taus_vTrtau!d _onVq "u!f

ia10odmq`!a%njd ej`!bVa

j`!b u!Vece"n

IA(x)dmq/cegd e"nodmkc`!_uzvxVe"ky`!d _e~

g[ 5)*E[)*¨H('P C l C .Ü KJgH C \ C E[¨X)*(X?()E C 5)*Pal=()k[ H\[!E[ C '[wNGX|E[*

H0 : β = 1[5? C )* HIEF ; * E[(*5)*Pa%k[ H\[h[5-(YY H\INZ $5')

KDF

M Eh\7E E H|<k E[H)* .E Hj-' g[\77 C 'PQ?)_ 5)*Paa C H'FF C E[WEa)*WE[(*WE[57 *')-G .-(F @dc(c X?)* wF g[IN )*W)*X?()EF C E[W=(')E[H('P C ¨g[ C '[ZNGX?E[* )* HIEFT .E["-7'!7E[

DF\7E E H"5)*P

*Ph)Ë[5 C E[ H()*)**X? C F C & H)* .E H|-' KRJG @ w @ n ^ ; C FW @ @ ;H()*)**X| C F C &E] * & C 5H C HgI-Z5 n(n n ^ w C F n(c X?)H C M A ¬E[&()*dkgE[a?[5-G (')% 5)*Pa% C H)\ C Ph)*(I )E C F(Pk+ (E[X?)*H C \&(¬)* HIE C ?E[ C '[wNGX|E[* *[('F~Pa(' C XX)* ; Ph7E.NWE @ ^ v C F @dc X|)H C v)**X?HIE .-(.N( g[]-'Y CWU KJ©¨ ;HIF¥E[ @ ¨^ C F @dc X?I) H C _I-( ug[ C .N H*WE[57 *[dka

n J


* &([ZE C F C HINaEdkg)*Fj!)E C F(Pk+ H* A Q Gg[ ¨ ¨F'E!E[E)* C &])E C F(P;¬HIYH'*FwNWE[" & F Z;¬)* C H!|I kj C

λ0 C F

λ1

jI=()*E[*~)**'.EW)*T C E)*X)*IEF .h akj()E[Zk[ TH C EPaXR7E C & *(PaH\)Ek[ H\[~ C O ' C HQE[]&()*<kgE[© 5)*PaY C E[QPh)*I g[)*_)*! kjWDNGX?%HIE()* g[5)*DNGX?!H'*E[!&()*dkgE[5)*PagEa?!_)E C F(P k+ k[)*E["*H C F NGX|aF Ew' .E_\7E C )N©|[5d-G (') _g[ K**'PaX;E C M )E C F(P C *!¨E[*)*H[©?[5-G (')Y%X?E C E RlH C *'Pa)* Y_ NGX|Q C !HIE() .-( C

λ1|E[][ &([)

λ0E[aPa()*aX)*(5a .! "E[57!E[h&()*dkgE[ )E7Ea 5)*Pa! ])E C F(P k+| g[

H C ?T* C ZN¥H(PaX5)* C & H* A Kλ0 = 0.4

Wλ1 = 0.2

M k .E[H* A Kλ0 = 0.8

Wλ1 = 0.2

M g[)*¨=() w'5λ1H* A [5_X)*(X|()E C C ) E[.I-Z+k[)*

H0H('F©? HHX;EF ¬k[)* C H* A E[QX)*(X?()E C %E \7E E H=()k[ H\[©E[H0

[5Eh?])* HIEF© w' .E]R)*&() C E[]E[)[5 C F ¬[ &[T*)*H[© C E C * .E HIE .-("H C *'Pa)**w C &_=() dk+)gX)* H" C -((.-Zg\7E C )NW&()*<kgE[)E7E ¨g[ ?H'*"]*'HH*=' 5)*Pk .E[Wdkj)jX)* H+ ¨-()Nh .N EQ?*'HH*=' C E[ C GX?)* GFv .-( C

λ0E[hX)*(5 DN©E[57!E[h&()*dkgE[ 5)*Pa! !\7E C )Nu C H)**

Cλ1 Wg[ !H C |h* C ZNuH(PaX5)* C &H* A*A*A K

λ0 = 0.8Wλ1 = 0.6

M k .E[ H* A Kλ0 = 0.8

Wλ1 = 0.2

M ")*¬=()Yw'5λ0E[QX)*(5 .DN\7E C )N&()*dkgE[~)E7E

_[ &([) C H* A*A*A k[)*λ1 R)*&() A

λ0 C F

λ1 C H)**T7_E[EPaE Pa

E[W;¬HIQk C Q?WH) ©I-()E[* C hH C H C H'FhE[57λ1XRNGQTPa()*

PaX?()\ C )*(E[5 Cλ0FG)*&Z)*F C &E[+&()*<kgE[Q?[5-G (')!5)*Pa g[ I-G F C

.lH(PaX5)* C &QH* A A*A 5 C F A*AA ;k[)*E[ &()*dkgE[/5)*Pa+?H(PagPa)E C FPa()*\7E C )N

λ0 C F

λ1 C H)**"ZNW\[ \7Pa!*(';E C 'P |)

C )E.N . H C ?H C H'FF E[57QE[&()*dkgE[ ?[5-G (') 5)*PaQ C I .E[) \<E C )N C () C C D\7E C )N( VYWE[©)**'.E*[dk 5)*Pa j&()*dkgE[ )E7EFIX? C F CE[TH\[5)EHIE)* E HhE[TPh)*Ih' C F)hH C * F)E7E C A E[TH* A A*A j C F AA*A)* H C * F)*F C ()*PhhK= C H C E)E EH* A M ¬E[ )**'. E[ * PQ'R7E . C H C? *'PaPh)* F© C E[Qk+dNTE[57E[ &()*dkgE[u|[5d-G (') 5)*Pa )E7E[)\7E C )NE[5 CWC C D\7E C )N( g[G' GE[* PQ'R7E . C Fw C +X)*d-G FYI-G F C HY=()¨*'XX?()E C & )E7 lk `%)*(X?()E C 7E )*<kgE[ \

V C E[)w'E C E[57)* * .E[)*Q)*"F Z;¬)* C HY C 5)*P &()*dkgE[T C )*R7E C E5)*P * A k ?]H\[HFu C X5)E H'R)gk[IE[)F Z;¬)* C *)*H\[© C E C * .E ";¬HIE["&()*dkgE[)E7E /5)*Pa C Fk[IE[)E[)*")*"F Z;¬I)E C ;¬HIE C 5)*PagF Z;¬)* C

n e


* ADC ()*F)QE©*[<kE[*;¬HIE E[ 5)*Pa )*WF .-G FF C \TE[)*W&()*('XQk .E[)**X?HIE E[ )g* " C H\[X?)* wFv %g[!)**'.E)* &( .-Z C C U e;

U e; )*dkgE[ 7E |$ )*POG | C FTOG)*H\[~ij(E$ )*Pa

aOGPh S F 'P l)*&(

i+* Pa C EF Pa C \F P_ C EFi+* A c c Je( c c c U c c;@ J c c eZ n c c(c U c c e(e ci+* A*A c c e @ c c @ ^ c c;@ J(^ c c U @ J c c(c(n(nc c e((i+* A*AA c c e( nc c ^ n c c(c ( c c eZ(J c c(c ^ cc c eZi+* A c c eZJ cc c ^( c c c;@(@dnc c e @ U c c(c nc c e c;@

a _uqwd flrVp dmk#d `Ci*'T`!_ nodmq`!d e.Vdmqwb $ta#`=aae qwfhcp p 'fla%nod Vf ce"n)pmcua "u!fhq%'`!bVal`!_`|cpe Vf-$tau9_v "u!fhqsb"cq $taaeaa` "cp pmijnod $dmnoa%nd e `!_ `|bou!aaSr"cuw`|q~

g[¨-()E&(&()*dkgE[")E7EGE[%HX .\EwHY C &Z7E .-(.NYH()*)*R7EF k .E[E[ 5)*P * C H* c c Je( K=*Ph M c c;@ J K=PaF 'P M c c(c U)K=R)*&( M =()H* A c c e @ K=*Ph M c c;@ J(^ K=PaF 'P M c c(c(n(n K=R)*&( M =()%H7E AA c c e( n K=*Ph M c c(c ( K=PaF 'P M c c(c ^ cK=R)*&( M =()¨H* A*A*A ; C F c c eZJ c K=*Ph M c c;@(@dn K=PaF 'P M c c(c n K=R)*&( M =)jH* A Q g[ YH()*)**X? C FEaE[QIH C (Pa H] C E' .E . C E[57*Ph 5)*Pa&()*<k E)YE[5 C R)*&(5)*Pa ADC &( C )E ¬E[ \ C F5)*F~FI-G R7E C FH)**]YE[ 5)*P* Q C H)** ]g[FH)**"=)*(P *Ph|E_PaF 'P D* F gw' .ER)*&(;k[I)EE[ \ C F5)*FFI-G R7E C?E[g&()*<kgE[_)E7E%¬PaF 'P * F_ C F_R)*&( 5)*Pa)*g* Pa ) X5)E H'R)* N!=()[ &([λ0 g[ C F H7EE[57*Ph15)*Pa¨)*gPa()*+[IE)*(&( C ('¨ C E[ )%&()*dkgE[a)E7EE[5 C

R)*&( 5)*Pa &Z)*F C &u*Ph 5)*Pa \[-Z)E&(&()*dkgE[¥)E7EYE[HX .\+EGH\ [ &([) =()[ &([©*)*H\[u C E C * .E Yg[ H C ?Q* C wNE[Q*w' C H c c Je( K=H* AM c c e @ K=H* AAM c c e( n K=H* A*A*AM A l C G(w+7+H* A ; .EjPa C c c eZJ c *PajEQ?H(*E"E[57¨¬H* AA wg[ X57*E) C %*H)%=()%PaF 'P D* F5)*Pa .E[_dk*)*H[~ C E C * .E K=H* A C F A*AM ?E[ -Z)E&Q&()*<kgE[©)E7E )*]E[QR)*&( K c c;@ J C F c c;@ J(^ M ADC H* A*A*A K c c(c ( M . E[]*Ph ij(PaX5)*FEWH* A K c c;@(@dnNM C _H C H C H'F E[57E[_&()*dkgE[u)E7E jPaF 'P D* F,5)*Pa C &Z7E .-(.N©)*R7EFEQE[ *)*H\[ C E C * .DNhlE["HIE'5¬H'E(Pa)*

λ1 %V C ;¬HI

λ0 +[5)*F.Na-G *

$5()gR)*&( 5)*Pa | NGEPh7E H" C O ' C H"H CC .E[)g?"FIEHIEF=()λ0C ()+=()

λ1

n U


g[ C O ' C H¬*)*H\[h C E C * .E % C \[ 5)*Pa Z&()*dkgE[a)E7EF Z;¬)*¨Pa C &E[E[)*&()*('X " \[© C H)** C &W*)*H\[ HIE .-G .DN K9=)*(P H* A EH* AA*AM v*Ph 5)*Pa&()*<kE) % C F PaF 'P D* IF 5)*Pa"E C F ET&()*<k*]w' H\w.N( l)*&( 5)*Pa! ;[ .!E[Pa ;Fa;¬HI¨E[57¨E[ C H)** C *)*H[WHIE .-G .DNQ=)*(PH* A E]H* A*A C H)**E[ )&()*<k+\[ Z';j=')E[)% C H)** C *)*H\[hHIE .-G .E jK9=)*(PH* A*A E"H* A*A*AM FH)**E["&()*dkgE[)E7E ?dk E[" C .E ?I-ZH* A A YE[&()*dkgE[¥)E7E 5)*Pa YF Z;¬)* C a* a)*H(PaX5)*F ¨*Ph 5)*Pa [5-ZE[R)*&( &()*dkgE[ )E7E g[ )Q&()*<k+\[ )E7E_)*|('; Dk HQP 'H\[ QE[&()*<kgE[)E7Eh"PaF 'P * F 5)*Pa g C FPa()*E[5 C E[)*E Paa[ &([)_E[5 C E[T&()*<kgE[)E7ER)*&( 5)*Pa

>?8?sGI4<¤ sG>?4g[uHX .\EwHH\[5 C &(HH()*F C & E C -(EPa C ADC H\[ X?)* wF E[~HX .\EGH\*[)* C wYZNT_H C \ C Y)E7E!%FX)*H R7E C A E[!HX .\EGH\g?dk3 .EPa C P]'P <aH C *H<E[ 5)*P3[5E ; .lE[¨Ph)*I VY*[dk C |<-(*Ph 5)*Pa&()*<kE)jE[5 C R)*&(5)*Pa wE[57+ G*Ph!5)*PajPhYR)*&()¨ C -ZI*EPa C E+)*7E .-ZEE[ )* 7 A E') C (';E[57¨ C *(';E C 'PQ|)* wR)*&( 5)*Pa% C -(¨Pa()*gPa C IN w';E[] C -(EPa C *Ph 5)*PaY R)*&()X?)Y' C .%HX .\ $5()Y 5)*Pa C -(EPa C ¨[ &([)=()j![ &([h*)*H\[ C E C * .DNa7E[X?E C E R|H C *'Pa)* Y Z;¬)* C Hj?IDk+ C5)*Pa)* &(&()+=()g C E C * .-(.NWE)*H[ C &aHIE .-Z H'E(Pa)* g[hFI-((XPa C ]jE[ad-()E&(a C -(EPa C ."X*EF !*( Fu C C $ &(')*_U KJG g[!F5*[F C g*[dk E["Pa C Pa C FPh ; Ph C FE["F*EF C g)*X)** C E[\ C F5)*F¥FI-G R7E C Y')* C &~E[5)*_=IkX?)* GF E[)* a~)E C F(P C H)** C FFH)**_ C -()E&( C -ZEPa C " C =(')Ph7)EIE ]dkjI-Z) E[ ;¬H!H CC ?7*E)* ';EFaH)*.N]E"E[*)*H\[h C E C * .E g[ *Pa¨P 'H\[aPa()*gE!|Y Dk+7D\&(F'EPa C X)*GH*YHH()*F C & E E["dk C -ZI*EPa C .I-Zg C X?)* wF

t = 1

ij C H) C C &E[¨=')E[)F-Z(XPa C ?-Z)E&(j C -ZEPa C ( .?H(Pa)*R7EF!EYE[*)*H[ C E C * .E jX|E C E R7v C FHIE'5¬H C *'Pa)* ¨$ )* G .+H C | C EFWE[57+E[E)* C &E[E[ C &]k+d-(;E[57gwHH')*79E)jE[ F'EPa C +X)*GH* 5FX? C Fg C

λ1

g[ O 7*Ek+d-("H C ?"(*)-(FT C H* A C F A k[)* C E["Ph)*IE A*A C F#"sbVa $cp Va%q1qwbV_ /e-cu!a7`!_`|cp d e@$a%q`!flae `'Td ~a~d e@$a%q`!flae `SrtauSVeVd `_vskcrVd `|cp fVp `!d rVp d a%n($i `!bVa

kcrVd `|cpq`!_Vk! ~

n ^


0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

λ0=0.8, λ

1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &(')* U KJG%Vl-()E&( ADC -(EPa C

n


A*A*A E[]k+-Z[5d-( h[ &([)X?| C -Z)E&(¬ C E[5)*YE[)*QH* 5)*Pa C -(Pa()*"Pa C INE[][ &([)

λ0 C F

λ1)*|EaE[57H* A K JG Z c ^ M H* A*A Ke; KJ @ U M

H* A*AA Ke; U(Uw7U M %OG C HYE[ 5)*Paj C H* A 3 C -Zg C -()E&("e; @ (eZJ"k[ H\[ jPQ'H[Pa()*E[5 C C H* A C FPa(7PQ'H\[ C H* A*A .g*PagE[57

λ1[5 E)* C &

C O ' C H! C E[!-Z)E&!Pa(' C gPa C IN*X? C Y C H[Ph)*I g[I-Z5)*H\[FW C E[RX?)* wFa E)* C &(.N C &Z7E .-(.N )*R<\IF_E

λ1 g[Y[ &([I*

I-(gwHH')*_ C H* A K @ K^7U n M =(dkjF ZN H* A K @ c UZ cNM H* A*A K c K @ e cNMH* A*A*A K c K^7Uwê M C W)** C =()!E[ ])*R7E C *[ X PhdN |hE[57Q C E[h* P 'R<E CPaGF 7 C -(EPa C X?)F C .E C FX| C F%X?(* .E .-(.N" C X)* E% C F]E[+*(F]' C .E C FC &Z7E .-(.N C E[QX)*wF'HFu' C .E ADC -(EPa C "*WFX? C F C &Z7E .-(.N C 5)EP * *"E[57%=()%R)*&( 5)*Pa% C -ZEPa C ¨X|)' C .¬HX .\ %dk+)E[5 C =()%*Ph 5)*Pa ADC*(';E C 'P |)* ?[<kjI-() ¬R)*&( 5)*Pa C -ZYPa()*!Pa C INE[5 C *Ph 5)*Pa 5k[ H\[Ph | C F' .\ N 5 C PaX?()\ C gF E C HIE C C !;¬HY C C -(EPa C EPag=)*(P5)*Pa[5d-G C &!P_()*Ph7EH\[ C &"X)*(PavFPh C Fh C Fh*'XX.N_ C Ph)*(IE%k .E[h"[ &([*)*H[W C E C * .DN_?H'* [ &([ O 'HIE'57E C jH'*FZN

λ1*]E[57jE[INa9E C H CC

*jE[ )Q(';EX';_H(PaX.IE.N( V &©F Z;¬)* C H?IDk+ C *(F C F X)*GF'HF (';EX';(IXj C -ZEPa C ¨dk|H'* 5)*Pa%F C ¨ ;X?HI+"R)*&(+ C H)** C FPh C F_=()E[C GQX|)* GFv hg[h*H C F ;¬HI]kj()*w] C E\[_(XX?(* .E_F )*HIE C ][ &([

λ1F

E R)*&()a\ C F5)*FFI-G R7E C C F +E[)*I=()*+E *X)*F C C -(EPa C W* E[57E[)*)**(PagR)*&( 5)*Pak .E[_[ &([ E\ C -(EPa C =()*H C &"d-()E&( C -(EPa C ¨'Xv ij(PaX5)* C &TH* AA*A K

λ0 = 0.8Wλ1 = 0.6

M k .E[ H* A Kλ0 = 0.8

Wλ1 = 0.2

M k .E[)**X?HIË"E[X?7 ?E[k+-(wE[X?(* .E .-(;¬HI¨

λ1*Pa%E!F(Pa C 7Ek[)*

E[ -'"7gE[" C FE[")*' C *PaE_? C &Z7E .-(.N";¬HIEFwNλ1

VYY ;X?HIEF ¬E[]\ C F5)*F©FI-G R7E C E[Q-()E&(] C -(EPa C C H)**Y Cλ1? *

.j C H)**+=)*(PH* A EQH* A*A*A C FhE[\ C F5)*FWFI-G R7E C C H* A 3 jXX)* w Ph7E.N E[ EPa + C H* A g[ + +*Q-7 Fh=()Ë[ GE)*Pa-7' * ;Ph ; Ph C F Pa C Pa? C -(EPa C % C H\[_Ph)*I C + C E)*E C &YHI% kj()E[Zk[ C E C & ADC E[_R Ph)*I"X[5*lE[_F Z;¬)* C H_|I kj C E[_Ph ; PQ'P C F~E[a-()E&(_ &(&()QE[5 C E[F Z;¬)* C H|I kj C E[Pa C P]'P C F E[T-()E&( g[ _;¬HIh E[ E)* C &(g C H* A*A C F A*A*A Gk[)*E[ *)*H\[ C E C * .DNhE["HIE .-(H'E(Pa)* λ1? )*R7E .-(.N[ &([v g[QNGPaPaIE)NFH)**"

λ1FH)**3K=H* A M ¬ C FTE[

X[ C (Pa C C - C *[gj?E[W*)*H\[ C E C * .E λ0 C F

λ1FH)**3K=H* AM GV R)*&(

NGPaPaIE)N©Pa C YE[57 E[)*_)*Q=Ik 5)*Pa C -ZE C &PQ'H\[uPa C IN© C FuPh C N 5)*Pa

n


C -(E C &_. .*\.YPa C IN( ¨OG C H )*F;NW*[dk C ?d-Z [ &([λ1-Z()*g HIE.N

E[ %E)*'HIE')E . C *')*X)* * C & E[57 Z=()% C \ C Hw C H* A (k[)*E[)*)*Pa*E.NX57E)* C C &"H'E(Pa)* G C -(EPa C +%k+.?X)* Ej C F 5)*P* )*YPaw'5.NF E)* ';EFv A ! C -(EPa C h)*&Z)*FF )*)**X?H\ -Z©"E[ 5)*P * E[~X57*E) C ]$ &(')*TU e h(;\ C Fv VY)*F;N¥Pa C E C F |<-( .W akj()E[Zk[ TPhw C & F E C HIE C?IDk+I C E\ C -ZEPa C " C Fu C -(EPa C "X?)' C . ¨HX 7 g[ *( F© C ]*[dkE[YHX .\|EGH\_E[ 5)*Pa G*()EFW C *H C F C &Q()*F) g[H)*dkFWX?( C EjPh)*wE[¨-'5 C -ZEPa C X?)' C .5HX .\zK=PQ'.E .X .F!ZN J c(c =()?EE)H(PaX5)* * CM=()15)*Pa%E[57¨)*g C E[gPh)*(I¨7¨ &( .-( C X?( C ?E Pa K

t = 20; 60; 100M X LH\[

X?( C ¨vE[H)*dkFhH()*)**X? C FjE! C 5)*P C E[*( Fa C VYE[ C 'P |)¨ 5)*PaX*EF© w' .E]R)*&(¬hH)*dkF~Pa)*&( Yg[]-'Y C E[][()* C \ ; Y C F H7EE[ C 'P |)HIE .-( 5)*Pa Vg!E[ 5)*]&(R C HE[h&( C )E¨X57*E) C !* Pa .R7) =()!H* ©OGPh 5)*Pa! C -(Pa()*"Pa C INX?)' C .YHX .\vE[5 C R)*&( 5)*Pa +g[]*[5X?]E[]FEY*a*[dk [ &([)+-)* R . DNh C -ZEPa C X?)' C .HX .\¬=()g*Ph+5)*Pa 5 C F .*[dkY)*R7E .-(.NH)?()*F)E[!Ph ; PQ'P C FTPa C .PQ'PPa(' C E*X? C wNE[5)*Pa VY"X?( C EFu(';!7)E. ) vE[_F Z;¬)* C H" C HX .\EGH\w! C E[5)*!X[5*_jH* A)*.*jE[5 C C E[E[)jH*g C X[5* A ;g[ jH C ?Y* C 7jE[*(X|YE[*( F C jVYE[!Ph)*(IFI-((X ¬79E)X[5* AA K

t = 60M Pa()* 5)*Pa)*! C E[!Ph)*I

g[Ph ; Ph)*H\[FaZN *Ph 5)*Pa[5d-(g C H)**F_k[)*%E[(*g?R)*&( 5)*Pa[5-ZFH)**F * &([ZE N( ij(PaX5)* C &5)*Pa!+E[hEPaa* .!H C ? C EF E[57!E[(*5)*Pa"E[57][5-(h? C E[aR)*&(5)*Pa" C

t = 20)*a C

t = 60 C .NuPaF 'P D* F

C F*X? C FTPa()*" C C -(EPa C E[5 C C E[!X)*I-G .('X[5* C .NhE[(*5)*Pagk[ H\[[5d-(Q&()*dk C )*&(] C X[5* A*A *X? C F~ C

t = 60h*Ph)YPa(' C YPa C INE[5 C E[

=()*Pa)*.N~R)*&( 5)*Pa! Ct = 20

ADC X[5* AA*A gH* A )*F'HIE C C 5)*P * aH C?!(*)-(Fv gg[)*] C C H)**! C E[!'XX?)?(' C FT C -(EPa C *Ph 5)*Pa ';¨E[YFEj)*Pa()*H C H C E)E7EFW C E[Ydkj)j)*; S F 'P D* Fh C FhR)*&( 5)*Pa C -(*gE[5 C C E["X[5*?I=()* ADC H* A*A K

λ0 = 0.6Wλ1 = 0.4

M w C F_H* AA*A Kλ0 = 0.8

Wλ1 = 0.6

M 5)*Pa)*g C GE[)*X[5*gPa()*[\I)E&( C ('gE[5 C C H* A ADC X[5* A H* A*A C F AA*A ; C -(EPa C X?)g' C .HX .\¬ g*gF *X?)**F=()g[ &([)+E)*H[ C E C * .E %g["|()*F)*E[] j Vp `!d rVp id e.$t_`!b d $a%qz`!bVa1`!_`|cpNd e0$a%q`!flae `DqwbV_ /ed e d Vu!aX"~ o~

n


0 2000 40000

50

100

150

200

λ0=0.4,λ

1=0.2; t=20

0 2000 40000

50

100

150

200

λ0=0.4, λ

1=0.2; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.4, λ

1=0.2; t=100

0 2000 40000

50

100

150

200

λ0=0.6, λ

1=0.4; t=20

0 2000 40000

50

100

150

200

λ0=0.6, λ

1=0.4; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.6, λ

1=0.4; t=100

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.6; t=20

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.6; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.8, λ

1=0.6; t=100

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.2; t=20

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.2; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.8, λ

1=0.2; t=100

%HX .\ ;*()EF W · % C -ZEPa C 5X'H K9E PaJ c(cNM$ &(')* U e; ADC -(\P_ C YX|) C .%i+X .\

n(n


H)*<kgFF X|( C E )*_* H)E[5 C C H* A l C Fu C E[_H* A*A C F AA*A k[)* E[*)*H[W C E C * .E j)*Y[ &([) wE[ C 'PQ?I)+7 5)*Paj C E[YPh)*(I+)*Y* ADC X[5* A*AvE[H* A*A C F AA*A G C -(EPa C +v*Ph)5)*Pa ¨[ &([)%E[5 C C X[5* A G C FaE[)*)*Pa()*hR)*&( 5)*Pa ADC X[5* AA*A k[)*E[-()E&(HX .\jEwH [5 FH C F C -(EPa C _X?) ' C . YHX .\j Q C -()E&(*Ph.)!E[5 C C E[X)*I-G (' X[5* VR)*&(QX)*(X?()E C 5)*Pa [5 )*F'HF C -(EPa C "EPa C P]'P I-(% C H*A g[aPh()F Z;¬)* C Ha|I kj C H* A*A C F A*A*A C F H* A E[57 k .E[ C H)**F*)*H[ C E C * .E " C X[5* A*A*A gH* A*A C F A*A*A E[a-7)* R DN~+ C -ZEPa C ]X?)' C .HX .\l*PaYEW?QR)*&() ?';YE[)*_)*]* 5)*PaY C -(E C &WPa()*!E[5 C E[Pa C P]'P Pa(' C +E[5 C C H* A i+* A 'P_ C 7ElE[+;¬HIE%()* &( C 7* C &=)*(P

λ0 C F

λ1 g[j-)NG C & GE C 5E[

C -(EPa C j H'*FZNλ1 ADC E[)*X[5*+vH* A C F A E[YH)*dkFW7X?( C E

* Pa )+ C .E GE C Yk[)*Y C H* AA C F A*AA E[)*] _F Z;¬)* C X57*\I) C λ0

)**X? C * =()%E[F E)* ';E C k .E[ C E[?()*F)*¨FIE)*Pa C FhZNλ1 %$5() C H)** C &

λ0 C -ZEPa C %X|)' C .|HX .\;XX?)*E?+Pa()*¨H C H C E)E7EFv g[ Pa C E[57

=()¨ C -(EPa C +X?)j' C .jlHX .\|][ &([h*)*H\[ C E C * . N_X?E C E R|H C *'Pa)*+[5E[Y;¬HI+E[57 5)*Pa¨?[5-ZPa()** Pa )|H'* vE[Y)E C F(PF E)* ';E C C IkH'E(Pa)*gE 5)*Pa

!x<2 4< :5>¦swx<z2|x7¤ :5>y(s

]*(Pa GE C ;X)* Ej)* O HIjE[HX5 .DNQ 5)*Pa%EQF'¨E!E[ C -G )* C Pa C \H C F .E C OwE'F;NG C &©E[ )QFI-((XPa C _ .Q Q)*Ph7)E<aE[57QE[FI-((XPa C X)* E" C FuX?)=()*Ph C H C ! *PaGE[uE[ FI-Z.(XPa C "E[ HX .\EGH\| `)E H')*.N C E[5)*"Ph)*I"X[5*_ C H C (*)-(h C F'EPa C "X)*wH*"E[57 +E["Pa()* F E C HIgE["[ &([)+E["*)*H\[T C E C * .DNWX?E C E RvH C *'Pa)* g[aFI-((XPa C !¨E[ad-()E&(_X)* E! C FuE[_)**'.E C &Pa*')*_ 5)*P*'HH* X?)=()*Ph C HK=*( F" C M dE[ )lPa C Pa C F]Ph ; Ph K=F5*[FQ C M C F!E[ )l\ C F5)*FFI-G R7E C K=F*EF~. C M )*Q*[dk C C $ &(')*YU U C F~U K^ ¬)**X?HIE .-(.N( "lkjWk+d-(GHH')j C =(')jH*j=()E[-ZI)\7&(X)* E+k+?¨=()E[d-()E&(YX?)=()*Ph C HI g[5)*hk+-ZTGHHI')E'h C E[?&( CC C & K= C E[5)* @dc X?)* wF M A W _Pa()*F E C HI =() [ &([)

λ0¨ * ._ Pa(E.N H'*FwN E[*)*H\[HIE .-G . N YX?E C E R

H C *'Pa)* g[W\)* C &7\[ gE[Wk+-ZFX| C F_X?(* .E .-(.N C \[WI-(jλ0 ug[

@dc(c


0 10 20 30 40 50 60 70 80 90 100

0

5

10

15

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 100

0

5

10

15

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 100

0

5

10

15

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 100

0

5

10

15

λ0=0.8, λ

1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &(')*U U%V-()E&(!`%)* E

@dc;@


*Ph¨F Z;¬)* C H|I kj C H* A*AA C F H* A )**'.E]=)*(P E[F Z;¬)* C HW Cλ1 C

?E[H* g[!*H C FTk+d-(! _ C &_ C !wHH')*)* C &h79E)gE[!)E C F(P;¬HIEYE["R)*&( O <k(';Q+E[hX?E C E RH C *'Pa)* )*a)*R ;Fv ADC E[hH* A AA C F A*A*A E[h*H C Fkg-(g E[+Pa()*+F E C HI% C F [5Y[ &([)I-( E[g[ .&([)E[g*7)EH\[_ C E C * .E )* OG C H" C H* A E[!*H C Fk+-Z! O 7Y C H* A

λ1*PaEa[5-("E[!Ph ()

C O ' C H C E[ ¨kg-( g[ *)*H\[ C E C * . NalE[ HIE'5¬H'E(Pa)*7* ";¬HIE+E[I-(%jE[a-()E&(aX)* E!7 E[_ C F ¨E[_)*' C K

t = 100M hi+* A K @ e(eZ( M [5

E["[ &([I-( G=(dkjFwNWH* A K @ KJ cc M H* A*A K c ((e nNM H* AA*A K c K7U @ M g[h-Z)E&(_X)* E" C H* A AA C F AA*A FX| C F Ph C .NT C

λ0 C F )*_)E C (F

H* A K JG e c J( M H* A*A K JG K(J(^ M H* AA*A Ke; e(e c M ag[h[ &([)!-()E&(aX)* E C H* A K JG n c ^ M H(PaX5)*FEaE[(*!%H* A K9k .E[E[!\7Pa

λ1M )EIE' =)*(PE[

)E C F(P;¬HIF'gEE[+HIE[57 5)*Pa% C H* A ? C %=)*(PX|E C E RGH C *'Pa)* g[!\ C F5)*FFI-G R7E C X)* E 5 * E["F Z;¬)* C H" C X)* E|I kj C E[5)*Pag CE[jEPaPh)*(I 7 X|(* .E .-Z.N )*R<\IF!EE[¨*)*H\[ HIE .-G .E l;E[+HIE'5wH'E(Pa)* λ1 %g[)*I=()*E["dkj\ C F5)*FFI-G R7E C +(*)-ZF C H* A C F A ;k[)*

C H* A*A C F A*AA E[ F Z;¬)* C Hg?IDk+ C 5)*Pa)* &(&() %g[ g .g|H'*"=()+dkλ1Pa(E[]H'E(Pa)*Y)*Ph C .<NZv\_E[ )*'XX )**hE[57E[!H'E(Pa)Y5*

5)*P )*Ph C g)*R7E .-(.NhH C \ C =)*(PE["?&( CC C & ADC &( C )E vDk+X[5*"H C ?_F E C &(' *[F~ C E[ FI-Z(XPa C "jX)* E Y')* C &E[ 5)*¨X?)* GF (E[)* ¨ E)* C &")E C F(P;¬HI¨

λ0(k[ H[_-7 C *[j79E)?('; @dc

X?)* GF g[ C GE[Y C O ' C HvE[HIE'5?H'E(Pa)*j?IH(Pa+E)* C &()+.E[('&([_E[I-(%E[_-()E&( X)* EFX? C F"Ph C N C

λ0 "VPa()*]FI\ F~ C .NG* YE[

X)* \ NQ¬E[5)*Pa¨ X?)=()*PaF_E(&(IE[)k .E[_E[ C 7.NG* ¨vH C H C E)E7E C CX5&( @ ^(G g[uX?)=()*Ph C H©] 5)*P, WX?)F C .E C [ &([.N¥H()*)*R7EF k .E[E[~X)* E XyXg[)*I=()*$ &(')*U K^~E[57h*[dkhE[FI-Z(XPa C hE[©-()E&(TX?)=()*Ph C H * Pa )gEW$ &(')*!U Uhk[ H\[©X)** C EE[]X)* E C d-()E&(¬X?I)*=)EPa C H] YR)*&()=()j[ &([

λ0*QE[57jE[Y*Ph¨-'Y j(*)-(F=()jH* A wk[)* H* A K JG eUZ cNM

H* A*A K JG K n(n M H* A*A*A Ke; e n(c J M g[ -()E&(X|)=()*Ph C HY C H* A K eG c(c;@ M * &([Z\ Na*Ph.)¨E[5 C E[57gH7E AA*A 5jH'* lE[ E)* C & )*R7E C ?IDkj C X)* E]!]%aa ` "c`!d _e ; V~ #AB'or~JO01d e b"cro`!auSV~

@dc J


0 10 20 30 40 50 60 70 80 90 100

0

5

10

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 100

0

5

10

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 100

0

5

10

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 100

0

5

10

λ0=0.8, λ

1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &(')*U K^G%Vl-Z)E&(!`)=()*Ph C H

@dc e


C F X|)=()*Ph C Hl C E[ R"X?)* wF E[ -7' =()E[ H()*)**X? C F C &Ph)*IE")*XX)* ; .Ph7E.NaE["EPa g[w' 5E[!-Z)E&("X|)=()*Ph C H!Pa C &QE["Ph)*IE C E[R]X?)* GF @ KJ7Uw n K=H* AM c Z(J K=H* A*AM c K @ K=H* A*A*AM g[WR)*&(d-()E&(]X?)=()*Ph C H] (*)-(Fu C H* A K @ e(eZ @VM g[57 ?dk *)*H\[uHIE .-G .E HIE'5vH'E(Pa)*+NG FQ[ &([-()E&( I-Zv7X|)=()*Ph C H"7+E[ C FlE[ )*' C g["\ C F5)*FFI-G R7E C gPa()*E)* C &(.NWX|(* .E .-Z.Na)*R7EFE

λ1E[5 C E

λ0 Y Z;¬)

C HY C 5)*Pa X?)=()*Ph C H!)*" &(&()j=()[ &([)λ1|)*&('FT?d-Z" C E["H*!

X)* E g[jPa C Pa C FQPh ; PhE[+d-()E&(jX?)=()*Ph C Hj[5-(jEY?+* GE)*PaE[5 C E[(*Q%E[ -Z)E&(QX)* EZNTF C .E C Yg[ *W ;XR C E[Q* Pa )* DNE[ -'7gE[" C FE[")*' C C X|)* GF

t = 100

g[ w'E C .E[*F Z;¬)* C Hg C X)* Eg C FX|)=()*Ph C H )*YX?)** E C g()j .E[INH C -Z)*&(E]"H)\ C -' ¨*"F *H'**FW C E[ .E)E7E')* =-JVA|I+ K @dn(n M C F FIRT?BV?? K @dn nNM *'XX|()_X?I)E* E C F Z;¬)* C H C X)* E ]k+jQ C E[)5)*PH\[5)EHIE)* E H %g[! C .NG* glE["Ph)*IE)*'HIE')*!|dk *_&( .-(gI-G F C H=()+E["X?)** E C H!F Z;¬)* C H C X)* E X

WsGsw:x7y7r:5>¦ . sZ8?sG¡=2-¤ sG>?4dk E[QX)*GH* FX? C F" C E[Q*)*H[uHIE .-G .E %E[] kjWDNGX? H C *'Pa)*] ] C a+E[hPa(] C E)*E C &=<\')*]+E[h* PQ'R7E . C )**'.E g[ 5)*X?( C +E C E ¨E[57HIE .-ZH'E(Pa)*g[5-("QPh ()j C O ' C H C E[ I-(jkjv C E[+-)* R C H+ ;X? C F .E')* %g[g ;X? C F .E')*¨)*+[ &([ .?HIE .-(gH'E(Pa)**)*H[ak .E[_[ &([a C E C * .DN( g[57¨ 5)*Pa¨)*H(PaX?F E"*'XX.N E[ )&(wGF¨7¨dkX)* H wk[ H\[hH C C .N |F C .vX)*GF'HIE C H(Ej)*dk Z=() C \ C H GZNa C &Z&( C & C ] ;ij(PaX5)* C &"E[(';EH(Pa¬E[ X)*GH*¨=()¨F Z;¬)* C j*)*H\[W C E C * .E k .E[ )**X?HI_E©E[ C 'PQ?)QY Pa \7E . C C F CC <-77E C C F E[HI(a)*F'HIE CFjEaQ)*Ph)*<)**'. %VY.E[('&([ 5)*Pag*X| C FPa()* C ;E["-()E&( H()*F'HIE C g*Ph.)g C F=Ikj) C k EH\[ C ((&( g[5-Z"? C FI-((X?Fv g["-Z)E&( ;X| C F .E')* 5F Z;¬)* C E R7EFW C EQ Pa \7E -( C F CC d-7E .-(Y;¬()E )*"X)** C EF~g*( F C g C $ &(')* U; ; ADC E["I9gH('P C ;E["F Z;¬)* C H7EIY)**[<k C =()" Pa \7E . C l C F C E[a)* &([w"H('P C E[IN )*_*[<k C =()" CC d-7E C ag[H()*)**X? C F C &_Pa C .Ph] C FPh ; Ph] C F\ C F5)*FFI-G R7E C g)* )*X)** C \IFTwNhE[]=#aa d Vu!aX"~ * 'r~F#G*Go~

@dc U


F5*[F C F~F*EFu C ¬)**X?HIE .-(.N( Qij(PaP_ C EH* C C H)**Q C, ;X? C F .E')*F')* C &aE[5)*YDkjWPh)*IX[5* ?=(dkjFTZNTaFH)** C E[]RX[5* g[ C .E 5-'j=()+-5)*Pag)* c c(c J"=()+ ;X| C F .E')* C Pa \7E -(Y;¬()E C F c c(c ^=()! CC d-7E .-(a;¬()E]X?)]' C .]gHX .\ g[h-7'!k[ H\[ )*hX*EF)*aE[aE\ ;X? C F .E')* % E7 ;X| C F .E')* X?)]' C .]gHX .\PQ'.E X. .F wNuE[HX .\vEGH\| ij C H) C C &!E[Y ;X| C F .E')*+ C Pa \7E . C K=I9¨H('P CM w C H C *E[57j C H* A*A C F A*A*A wk[)*E[Y*)*H\[ C E C * .E +7)E[ &([) GE[Y C H)** C FhE[FH)** vE[ ;X? C F .E')*] C Pa \7E . C )*aR)*&()E[5 C C H* A OG')*X)* * C &(.N E[_X?~ C H*A*A*A dk+)E[5 C C H* A*A C d-()E&( Pa \7E -(];¬()E"7)E]E[Q*Ph C H* AK c KJ @ nNM <=(dkjF!wN!H* A*A K c KJ7U @dcNM C FQH* A*A*A K c KJ7Uw^7U M k[ H\[ 7)E-()N]* Pa )I lV+E[] C F[K

t = 100M |E[]d-()E&(! ;X? C F .E')* )*"E[]*Ph. C H* A*A*A K c KJ^ n;@VM

H* A*A K c KJ((^ @VM H* A K c KJ @dnNM %$5')E[)*Pa()*GE[ \ C F5)*FFI-G R7E C +[ &([)j CH* A*A C F A*AA H(PaX5)*F_E"H* A (k[)*E[)* %[5)*F.N_ C N F Z;¬)* C H?IDk+ C E[\ C F5)*FFI-G R7E C lH* AA C F AA*A +[ GE)*Pa-7'g*[dk ]F Z;¬)* C gX57*E) C [)*¨ C H* A*A E['XX|) GE)*Pag-')*gR)*&()E[5 C C H* A*AA (=()E[g<kj) GE)*Pa -'+E["(XX?(* .E +E)*' E ; C H* A*A*A E["Pa C P]'P Pa(' C Eg*X? C Y C Pa .\<E -Z;¬()E)* <kj)+E[5 C C H* A*A V C .NG* C & H* A *[<kaE[57

λ1H'*hE[I-(YE[T\ C F5)*FFI-G R7E C j *

E[_[ &([)λ1E[aR)*&() E[_\ C F5)*F FI-G R7E C C FuE[_R)*&()")* E[_ GE)*Pa

-' %Pa C PQ'P C F Ph ; P 'P ADC H* A E[5)*PaQ*X| C F c KJeZ(J C Pa .\<E -Z;¬()Eg C -()E&(k[ H\[ +* &([ZE.Na?dkE[" ;X| C F .E')*H* AA VggE[ C F E[h ;X? C F .E')* C Pa .\<E . C )* c e @ n lk[ H[ "E[h[ &([ Pa(' C ]%=(')H* ¨g[57

λ1 C O ' C HgE[!-ZI)\7&(" ;X? C F .E')*X|(* .E .-Z.N';* &( C )E7E

dk-7' 7!\[h C Fv ©g[WX| ] C O ' C HF ZNλ0 ©$5()![ &([

λ0E[h C H)**W

E)* C &() ¬ * ? C H* A*A*A E[]X? Y[ &([)E[5 C C H* A ¬ C F© C H* A E[]X? g* Pa )jE E[57 C H* A*A*A g[-Z)E&( ;X? C F .E')*a C CC <-77E .-ZW;¬()E *[<k~* Pa )]X57*E) C $ )* ¨ C C H)**W C

λ0 C H)**QE[hX? gE[-()E&(W ;X? C F .E')* %k[)*WH* A*A C F

A*A*A )*Qw' .E * Pa ) "g[ ;¬HI"E[57λ0[5 C E[ X?T*Pa" C .NTE? X)** C

=()<kλ0 +$5()g-'Y|<-(

λ0 = 0.6? =')E[) C H)**![5 C h;¬HIY C E[!X||

g[YFH)**79E)%E[YX| k+¨)*H\[FW H)*.N [ &([) C H*¨k .E[a[ &([λ0 %g[

d-()E&( ;X| C F .E')*)*E[ dkjg=()+.<kE)*H[ C E C * .E I G E ;H* A K c e n ^(^ M

@dc ^


0 50 1000

0.2

0.4

0.6

0.8

1

Imitation; λ0=0.4, λ

1=0.2

0 50 1000

0.2

0.4

0.6

0.8

1

Innovation; λ0=0.4, λ

1=0.2

0 50 1000

0.2

0.4

0.6

0.8

1


1=0.4

0 50 1000

0.2

0.4

0.6

0.8

1


1=0.4

0 50 1000

0.2

0.4

0.6

0.8

1


1=0.6

0 50 1000

0.2

0.4

0.6

0.8

1


1=0.6

0 50 1000

0.2

0.4

0.6

0.8

1


1=0.2

0 50 1000

0.2

0.4

0.6

0.8

1


1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &(')*U ;%Vl-Z)E&( L ;X| C F .E')*

@dc


H* A*A K c U(U(U cNM H* A*A*A K c UZ @dcNM g[-()E&(H* A c U(UZe(! C F wE[)*I=()**jE[5 C H* AA ';+R)*&()E[5 C H* A GV+jE[ C F 15)*Paj*X? C FPa(jPa C INa C H*A K c K^ @(@dnNM H* A K c U(Uw( M H* A*A K c U(UZ @VM H* A*A*A K c UwJ( M g[)*I=()*λ1[5 E[_Pa ;F~;¬HI!E[57" . X?(* .E .-(.N©)*R7EF~EE[a-()E&( C F C &Z7E .-(.N

)*R7EF EE[h ;X? C F .E')* 7]E[h C Fv Tg[W\ C F5)*F FI-G R7E C ] C H)**F ZN [ &([

λ1G C FaE[ GE)*Pa-'I¨ C H)**wk[)*E[FI-G R7E C ¬E[Ph ; PQ'P =)*(P

E[!-Z)E&("|H(PaR)*&(I)+E[5 C \[ FI-G R7E C E["Pa C .PQ'P=)*(PE[!-Z)E&( ij(PaX5)* C & Pa .\7E -(T C F CC d-7E .-(;¬()Eh C TH C *TE[57a\[T C H)**TF')* C &E[)*' C )*R7E .-(WEuE[ C .E -'_ R)*&() C ¨=(')_H*_=() Pa \7E . C E[5 C=() CC d-7E C .E[('&([E[Q*(';E!I-(*X? C C CC d-7E C E [ &([) C )** C Pa &([w|+E[57E[+ C .E R7Z-'=() CC d-7E .-(j ;X? C F .E')*%X?)' C .|HX .\)*¨R)*&()E[5 C =()l Pa .\<E -Z ;X| C F .E')* %V C 7\[I))** C Pa &([wl?E[57 CC d-7E C FEPa()*;¬HIE .-(%)EIE' \vE[5 C Pa .\<E . C dPa*')*F"ZNE[%FH)** C X)*GF'HIE CH(E &([ ;X? C F .E')*a C F C _&('5)E C E C PaX)*<-(Pa C _E[EH[ C ((&N( g[IN C .N~ C H)**_E[aX)*(5 .DNTk .E[uk[ H\[ C Pa .\7E . C ()! C CC d-7E C PhN?YH7)E)* IFh('; g[ D*'HH* YvE[Y Pa \7E . C C Fh CC d-7E C X)*GH*+)**'.E C &"=)*(PE[ ;X| C F .E')*Y gFwH'Pa C EF C $ &(')*U K C F U U $ &(')*jU K*[dkE[ C 'P |)| Pa \7E . C lK=*( F] C M C FQE[ C 'PQ?)| CC d-7E C K=F5*[F©. C M =()gE["=(')H* g$5()g* PaX H DN ;E[ C 'PQ?) CC <-77E C g PQ'.E X FhwNJ c C E[ 5&(')* %g[ C 'PQ?)jl Pa \7E . C ¨ jPQ'H\[R)*&()E[5 C E[ C 'P |)¨ CC d-7E C "g[ ()* &( C 7*Y=)*(P E[ )E C F(P X)EwH* E[57 &( C )E7E" Pa \7E . C k .E[ ©[ &([)]X)*(57 .DN( ©jE[ E[ C 'P |)Q Pa \7E . C ]]kj+7]E[ C 'P |) CC d-7E C C H)**QF')* C &hE[5)* kjWPh)*(IX[5* ADC X[5* A*AA ?E[INT*<kF<k C %g[ jH()*)**X| C FjE!E[X57*E) C vE[Y-Z)E&( ;X? C F .E')* ADC $ &(')*U .% *[<k C \[5<¨79E) EF;N C H)**g C E[ 5)*% kj"Ph)*IX[5* ZE[ ;X| C F .E')*FH)**! C E["RPh)*(IX[5* ADC E)*E C &(.NWE[('&([ ;E["X57*E) C E[ ;X? C F \')*Y C FE[ C 'PQ?)g Pa .\<E . C g C F CC d-7E C g)* C F C E H ij C H) C C & 5)*_E[ Pa \7E . C %E[)*T)*TJ(G KJ n(n ~ Pa .\<E . C C H* A J(JG K(J(^K=H* A*AM @dn Uw^ @(@ K=H* A*A*AM l C F J(G e c e n C H* A C -Z)E& _g[ C 'PQ?I)" Pa .\<E . C C H)**¨ C E[ 5)*¨X[5*Y C FhPa(' C E% C X?)* GF

t = 20E @(@ n 3K=H* AM

n ZJ K=H* AAM G U c K=H* AA*AM C F @ JG eZ K=H* A M A C X?)* GFt = 60

E[ C 'PQ?) Pa \7E . C ¨ C H)**+=')E[)+E eZJG K c K=H* AM J; @(@ K=H* AAM J7U n 5K=H* AA*AM

@dc


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.8, λ

1=0.2

Pa \7E . C w%% CC d-7E C$ &(')* U KG%Vl-()E&(!'P |) A Pa .\7E . C g C F ADCC d-7E C

@dc


C F e @ UZ K=H* A M vVg E[ C F E[Q-'")* UZ; @ e K=H* AM eZ^G e @ K=H* AAM J n K^3K=H* A*AAM w C Fh^ @ K^ n K=H* A M Zg[gE)* C Fa*[dkE[57%E[ C 'PQ?)%¬ Pa \7E . C FX? C F C &Z7E .-Z.N C

λ1 ADC H* A C F A ZE[ C 'P |)¨v Pa .\<E . C % E[[ &([I*

=() E[)* X[5* g[ C 'PQ?) ¨ Pa \7E . C Y C H* AA R)*&()E[5 C C H* AA*A=()g?X[5* ¨$5()jE[ H7EI A*A C F A*AA Q* &([Z+FH C C X[5* A*A*A H C ?(*)-ZFv ADC H* A C F A wk[)*

λ1 ¨<k Z\[ C 'PQ?)jl Pa \7E . C C H)**+EF .N_ C

X[5* ~ij C H) C C &© Pa \7E . C lE[aE)*H[ HIE .-G . N~+E[hX?E C E RH C *'Pa)* λ0*PaE_[5-(! .*E.;¬HI

g[ C 'PQ?) CC d-7E C Q Q*Ph)!E[5 C E[ C 'P |) Pa \7E . C ]?H'*E[X)*(5 N~ C CC <-77E C ]dkj)]X?)]F C .E C C d-()E&(E[)*)* c U n(n;@ CC d-7E C K=H* AM c Uw^ n e K=H* A*AM c e n;@ ULK=H* A*AAM C F c K^(J(J(GK=H7E A M ADCC <-77E C Q*©XX|)!E©FX? C F C &Z7E .-(.Nu C E[hE)*H[ HIE .-G .DNu+E[WHIE'5H'E(Pa)*

λ1 ADC H C E)EYEhE[ C 'P |)Y Pa \7E . C 5E[ C 'PQ?)Y CC d-7E C

FG C C H)**!*aEF .N( j$5() PaX. C .E[) C X?)* GFt = 20

E[ C 'P |) CC d-7E C =(dkE[()*F)j

λ1Gk .E[ c KJ c K=H* A%M c eZJ K=H* AAM c @ ^ KH* AA*AM

C F c KJ n K=H* A M C ()j C X|)* GFt = 60

k .E[ c U n K=H* AM c U n K=H* A*AM c K^7U>K=H*A*A*AM ; C F c K^7U>K=H* A M Gg[)*I=()*; C .N E[-()E&( C 'P |)j CC d-7E C FX? C FC &Z7E .-(.Na C E[*)*H\[HIE .-G . N_E[ HIE'5?H'E(Pa)*

λ1 %g[*)*H[HIE .-G .DNa

E["X?E C E RvH C *'Pa)* λ0[5 .*E.;¬HIg +\[ H*! Pa \7E . C

Y .-G FFa C E E[E[)*X[5* wE[Y-()E&( C 'PQ?)v Pa \7E . C % C Fh CC d-<\ . C )*X)** C EFa C gU U $5()H[_X[5*wE[gI9%H('P C H C \ C \[-Z)E&( C 'P |)+ Pa .\7* C ! C F E[a)* &([Z"H('P C H C \ C "E[h-()E&( C 'PQ?)!+ CC d-7E C CE["H()*)**X? C F C &_X[5*

"U U'PQ?)g A Pa .\7E C C F ADCC <-77E C `%[5*

a`%[5* A `%[5* A*A `%[5* A*A*A

i+* P C P C P Ci+* A @(@ Z^(J7U c KJeZe J; @ cc K^ c(c(n UZe; UZe c(cc K(^ n;@i+* A*A n e7Uw n c KJe(( Je; KJ( @ c UZZJ( eZ^G K^7UwJ( c ZUi+* A*A*A G K @dn c @ ^ZJ J c KJ(J c(nc U @ J @ e c U @ J( c c e ni+* A @(@ U(U(Uw^ c KJ c e J; @ n U c K^ @(@ J U(U KJ n nc K n Z

ab"cqwa%q$#B' # #B'Vce"n ###sk#_ $aus`!bVaSrtau!d _onVq

t = 1`|_E*.'

t = 34`!_EY*Y.'Vce"n

t = 67`!_E>*>V~

@dc(n


%U UH C 5)*PavE[ C F C &($ &(')*U Kjk .E[")**X|HIEgE[ C 'PQ?); Pa \7E . C A [ &([)W=()dk*)*H\[ HIE .-G .E W!E[ HIE'5 H'E(Pa)* $')E[)*Pa()*E[d-()E&( C 'PQ?); Pa \7E . C v C H)**=)*(P X[5*%EX[5* %ij C H) C C & CC d-7E C =() E[h-Z)E& C 'PQ?)"+ CC d-7E C C E[aX[5* E[_-7'! C E[_\ *[<kE[57Y C H\[©H*!E[)*] Y C C H)** ADC H* A |k[)*]?E[T&()*('XY%H C *'Pa)**)*H[hk .E[W][ &([a C E C * .DN wE[ C 'PQ?)j CC d-7E C ¨ C 5X[5*+R)*&()E[5 C CE[!E[)H* ADC E[ 5)*YX[5*5E[ C 'P |)* CC d-77E C g C H* A C F A*A )** Pa ) ADC v7\[I)X[5* |E["F Z;¬)* C H)*" &(&() C F=(.<kE["'*'5X57*E) C * E[]-()E&( C 'P |)7 CC <-77E C FH)**gE[!*)*H\[~HIE .-G .DNWE[!HIE'5H'E(Pa)*

λ1 C H)**

ij C H) C C &WE[ 7?d-ZDPa C E C FT-7)* R ¬*'H\[uHX .\l\wH\© C F©X)* E ¬E[)*[5d-( .k+NG| C F x;¬)* C ;¬HIE%E[Q*)*H\[uHIE .-G .E %E[]DkjW&()*('XH C *'Pa)*l C E[ )Pa C C F"I-ZGE[\ C F5)*F!FI-G R7E C )*7E[)**'.El C F H7E .*E.+;¬HI¨|E[HIE .-G .E .¬X?E C E R;H C *'Pa)* w';j HI)%;¬HI¨?E[HIE .-G .E HIE'5H'E(Pa)* g[ YFEaE[]H C H'* C |E[57YPa(YE[5)*P H\[5)EHIE) E H!FX? C F C E[ C 'PQ?)!gH'E(Pa)*!E[57][5-Zh| C )E C F(Pa.N~Ph7EH\[F C FE[57 ';NT&(GwFY=)*(P hH)\ C 5)*P ?H'* E[QX)* HI .H\[5)*&( "g[Q* .E'57E CH[5 C &( .% C QH C * F)*YE[5)*P X?( HINH C H) C C & ;X? C F .E')* Z-G ('*.N E[5)*Pa=(dk H)\ C E)E7E&N~ C FIE)*Pa C C &[dkP 'H\[~E[IN~ C E C F~E*X? C F C C *H')* HIE .-G .E g[ )a)\<\ . C \ C -(WPa()*Pa C IN¥ C .E[ ) C -G )* C Pa C " . )*R7E .-(.N' C \ E ¬ .

λ1 [ &([v Z-G ('*.N 5)*Pa F C

\(Q C EWHH(' C E[Q)E C F(Pa.NPh7EH\[F~H C *'Pa)*?H'*QE[ ) C 'P |) C F~|[5d-G .(')! ![5)*F \X)EIF HI VYQ)**'. E[)*W C ©5*h C k[ H\[ E[IN H C ' FE[ )E)E7E&( g[Y C .N *H')*HIE()%E!?\ C C E"H C * F)E7E C %E[ C 'P |)+E[ )!HIE'5H'E(Pa)* k[(PE[INuE)NuEX ZN t;¬)* C &dkX)* H j* F E[IN [5d-(aET C *')*hE[57!E[ )"<k C X)* HQ)*adkH(PaX5)*F EE[ )!H(PaX|IE .E()* X)* H ag[ " "-()NuF Z<aH'. \*~ .E[ )"H'E(PaI)E"*)*H\[ k .E[ [ &([u C E C * .DN C F wE[)*I=()*; C H)**H(PaX?IE .E C A vE[ )¨H'E(Pa)*j[5-(Y[ &([a*)*H[WH(E GE[IN\dN )*R<\ -Z.N C &u7 E[EPa5)*P |H'*E[IN¥)*5F.N C =()*PaF ?('; E[X)* H!+E[aE[)!*.)* ADC E[57]H*E[ 5)*Pa![5-(W*H')*hH'E(Pa)!5*aE(X?)E7Ea=)*(P C F E[hX)***')*WgX57E)* C C &H'E(Pa)*!k[©X?(** .NuH\[5 C &(aE[*'XX ) Y)*R7E .-(.Ndk" g[w' vE[)* C C F~E)*F'HQE[QX)* H PQ'H[u .E[HIE'55H'E(Pa)**)*H\[ak .E[a [ &([_ C E C * . N]=()%|I*E)¨(XX|()E' C .E dk+I-() E[ 5)*Pa 5E)E7E&NH C H) C C & ;X| C F .E')*Y*PagEa?! X5*E -Z"E)\<\I&NE

@(@dc


*H')*_()E* &([ZE N PaX)*d-(!E[ )Ph7)EIX?(* .E C ADC &( C )E ;X? C F .E')*)* C '*F©&&()**E -Z"E)E7E&NWE_ C [5 C H!H(PaX?IE .E C HIE .-(.N( A ] C E H E[57 C E[a C a[5 C F E[hd-()E&( ;X? C F .E')*] C H)**hλ1 C H)** Y'; C E[~E[)W[5 C F E[ C 'PQ?)W! Pa .\<E . C W C F CC d-7E C

FH)** j U K^Q*[dkgE[!-Z)E&( H()*F'HIE C X?) P_ .\7E . C C F CC d-7E CF)Edk" hg[57! X?(** E ."j PaX)*<-G C &WE[_EH\[ C ((&Nu)*aH' C EF .E[('&([C Yv7*EPaX;E)* =)*' .*='

U K^G%Vl-Z)E&(]ij( F'HIE C X?) Y)Ek∆H(X?) Pa \7E . C

∆H(X|) CC <-77E C

i+*i+* A c c(c J c c @(@(@ Ji+* A*A c c(c;@ e c c ((i+* A*A*A c c(c;@ c c Z^ ci+* A c c(c;@ c c (U

g["-()E&(H()*F'HIE C C )*R7E C E]E[X?(** E .j(;\ C FW jE)* HIE.Na[ &([)=()W CC <-77E C g[ Pa C WE[57 C -()E&(u H\[5 C &(~ C EH\[ C ((&NF'©E¥ C CC d-7E C F¨EQ!E)* C &()jFH)** C X)*GF'HIE C H(jE[5 C !H[5 C &(Y C EH\[ C ( (&N~H'*F ZNu C Pa .E7E . C ADC H* A*A Pa \7E . C kj" CC d-7E C )*_;¬HIE .-( ¨V3H)gNGEP H C H) C C & E["*)*H[ C E C * .E gH CC ?"(*)-(Fv U .'P_ C 7E_E[DX)* \ . N ;X? C F .E')* g[~-()E&(TH()*F'HIE C C )*R7E C E] C ' C .jvPa C IN_*X? C + C F .-G FFh C E! Pa .E7E -Z C F CC d-7E .-(";¬()E g*[<k C j$5)*(P C "' C .EX| C C C Pa \7E -( ;¬()EgE[]-()E&(H()*F'HIE C .+R)*&()¨E[5 C C E[H* CC d-77E C g[57g ; .+ jPa()* ;X| C * .-ZE C -( C CC d-7E C E[5 C C Pa \7E . C $5()Y Pa \7E . C YYkjY=()Y CC d-7E C C C -G )* C Pa C k[)* E[ *)*H[ HIE .-G NTE[_HIE'5H'E(Pa)*" )*R7E .-Z.Ndk*PaaE [5d-(T X?(* .E .-( PaX5HI_ C E[Td-()E&(H(h)*F'HIE C X?)a' C .a ;X? C F .E')* ~ GE C F E[ C .NG* ] ;X| C F .E')* E[ )QPh ()!FIE)*Pa C C EQ)*WE'FG Fv L ;X| C F .E')*! C *PEFX? C F Pa()*QE)* C &(.N© C X)* EE[5 C C 5)*P* FIRT?BV??UK @dn nNM \7EQE[57_X)* E_)*X?(* .E .-(.N )*R7EF E K7

@(@(@


U ;ïj( F'HIE C C F L ;X? C F .E')EI a∆H(-K= Pa .\<E . CM

∆H(-K= CC d-7E CM

i+*i+* A c ZJ( c c KZ @i+* A*A c Ke(( c ZÛi+* A*AA c K(J(^ @ c (Z(î+* A c (e(( c K n e(

a"sbVa)k#_ q` u!a%no"ky`!d _e"q cu!a fla%cqwVu!a%n rtau VeVd `g_vSd fld `|c`!d $a ;xp a#vY`k#_p VfleIAsce"nd eVeV_#$c`!d $aE;xu!d b `9k#_p VfleIA a10ortae"nod `!Vu!a%q~

h' C *WH C H C E)E7E C h[ &[ M C F g C *')-(ING C & E[T .E)E7E')* ?J1BDAYXIA K @dn(n M H C H'F_E[57aPa(aYE[PaX )* HjE'F a[5)*F.N C F C N I-G F C H=()E[uOGH\[w'PaX?IE) A*A [wNGX|E[* hE[57W CC d-7E C h)*TX?(* .E .-(.N )*R7EF¥E 5)*Pb* K= .Y .a QE)*'E[ C C .N 'X¥E uH)\ C F&()* M g[ a _* C C Wk .E[ E[ C -Z)** gD*[5X?F)*R7E C ?IDk+ C CC d-7E C C FH C H C E)E7E C =(' C FZN RFIACQ C FP FWXIRT?H K @dn(n U M $ &(')*U g*[dklE[E\( ;X? C F .E')* C 5)*Pa*X? C F! C -Z)E&( K9E[H)*dkF!X?( C E M g[ ;X| C F .E')*j)**()EFaZN HX .\ C FaPQ'.E .X .F ZN @dc(c =()%* PaX .H .DN( g[*( F C W*[dk_E[HX .\j\wH\wa 5)*Pa ¨)E C (F =)*(P E[*PhQE~E[R)*&(=)*(PE[I9E"E[)* &([Z LH[hX?( C ¨¬E[H)*dkFWH()*)**X| C FjE] 5)EP&( .-( C * I g[5&(')*]*[dkYE[57YR)*&( 5)*Pa*X? C F©Pa()*! C C d-()E&("E[5 C*Ph 5)*Pa A E[!E\ ;X? C F \')*)*Q C .NG*F=()F Z;¬)* C X[57EIE[Ph)*(FI-Z(XPa C | .H C ?!* C C $ &(')* U E[57F')* C &_E[ 5)*YX[5* ;X? C F .E')*!R)*&(5)*Pa)*©F *X)*(X?()E C 7E N¥dk H(PaX5)*FE E[ )WHX .\EGH\| ADC X[5* A*A ;X| C F .E')*g)* C )*.N_X)*(X?()E C E]HX .\ Zk[)*j CE[_R X[5*E[QE\ ;X| C F .E')*! C )* [ &([)X?)"' C "¨HX .\E[5 C C E["X)*I-G ('X[5* ADC +U K E[+Pa C C F \ C F5)*F_FI-G R7E C 5E[+E\; ;X| C F .E')* C )*)*X?()EFv X $5()YH[~H*_ C C H)** %E[_-()E&( ;X| C F .E')*"H C ? (*)-(F=)*(PX[5* A EX[5* A*A l C F FH)**a=)*(PX[5* A*A EX[5* A*AA lg[a()*F)"E[ ;X? C F .E')*" C E[ =') H*" F Z;¬)* C =() H[uPh)*I"X[5* ADC E[]=#"sbVdmqsb"cq/cp u!a%cnoi$taae4$dmqw"cp d a%n d e d Vu!aX"~ YV~

@(@ J


0 2000 40000

50

100

150

200

λ0=0.4, λ

1=0.2; t=20

0 2000 40000

50

100

150

200

λ0=0.4, λ

1=0.2; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.4, λ

1=0.2; t=100

0 2000 40000

50

100

150

200

λ0=0.6, λ

1=0.4; t=20

0 2000 40000

50

100

150

200

λ0=0.6, λ

1=0.4; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.6, λ

1=0.4; t=100

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.6; t=20

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.6; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.8, λ

1=0.6; t=100

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.2; t=20

0 2000 40000

50

100

150

200

λ0=0.8, λ

1=0.2; t=60

0 2000 4000 60000

50

100

150

200

λ0=0.8, λ

1=0.2; t=100

%HX .\ ;*()EF · · · ;X? C F .E')* 5E\$ &(')* U ; C FT$ )*POG

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"U KG%\ L ;X| C F .E')*`%[5*

a`%[5* A `%[5* A*A `%[5* A*A*A

i+* Pa C EF Pa C EF Pa C EFi+* A c e(( cMc c(n @ c KZ(^ c e(e @ ^ c K @ ZJ c KJeZ ni+* A*A c U c ( c @dc (e c ((Z^ c eZ(^ c n @Bc eZJ(i+* A*A*A c UZUwJ c @ e(U c n;@ UZ c U @ Z^ c Z @Bc eZ^(J ni+* A c UZe @ c @(@ U c c (eZ^(J c eZ n(c c @dn U c KJ(J @dn

ab"cqwa%q #B' ##B'ce"n# ##cu!a/u!arVu!a%qwae `!a%n $ i `!bVaDrtau!d _onVq

t = 20't = 60

'oce"nt = 100

~

5)*jX[5*-()E&( ;X? C F .E')*j C H)**YF'E] C C H)** Cλ0wk[I)E+ C X[5*

A*A λ1*Pa_Eu?E[Ph ()QFIE)*Pa C C _E[I-(7 ;X? C F \')* ADC X[5*

A*A*A v\[ C &("[5d-(_E') C F )*(' C Fv W$)*(PH* A EH* A*AA E[h-ZI)\7&(a ;X? C F .E')*FH)**]

λ1 C H)**

g[u)*7E C *[ X?IDkj C E[ ;X? C F .E')* C F E[©HX .\YEwH C FE[)*R7E C *[ XQ?IDk+ C ;X| C F .E')*j C F_X)* E¨)*g*[dk C C IU " C F_U n g[])**'.EY)*!)*X|()EFT=()gE\ ;X? C F .E')* K5)*YH('P C H\[©X[5* M k+Ig=()+E[" ;X? C F .E')*X|)' C .HX .\K=*H C FTH('P C H\[TX[5* M g[]H()*)*R7E C ?IDkj C E\ ;X? C F .E')* C FTHX .\ [ &([.NWX?(* .E .-("X?)F C .E C A E[H()*)*R7E C ?IDkj C ;X? C F .E')*hX?)h' C .aHX .\ C FHX .\¨ ])*&Z)*FF E[W)*R7E C *[ X C &(7E .-Z ©g[ C &Z7E .-(hH()*)*R7E C C H\[

"U ;ïj()*)*R7E C ?IDk+ C C F$ )*P OG a

`%[5*b

`%[5* A `%[5* AA `%[5* A*A*Ai+* E\ X'H E\ X'H E\ X'Hi+* A c n (e(eB c UwJ n c n ^ n(c c eZ^ @ c n e @dc c c @ ei+* A*A c n ^(eB c KJ( @dc c n (eZJB c @ ^(J @ c n c c c UZe(i+* A*A*A c n c Uq c @(@ e c n c ^ c KJ7UZe n c n ^( c c Ûi+* A c n ZJ7Uq c UwJ n c n UZe(q c KJZê c n @ c c ZJ

a"sbVa "u|q`Sk#_p Vfle d e)a%ck!b)rVb"cqwa qwbV_#9q9`!bValk#_u!u!apmc`!d _e $ a#` zaae "u!f qwd alce"ng`!bVa`!_`|cp a10ortae"nod `!Vu!a%q;Y`!_`|cpVAB'sce"n `!bVa qwa%k#_e"n qwbV_ 9q7`!bVa k#_u!u!apmc`!d _e $ a#` zaaeVu!f qwd aSce"n a10or ae"nod `!Vu!a%qsrtau/VeVd `D_vkcrVd `|cp ;xrV"kAy~bb"cqwa%q$#B'##B'"ce"n## #zcu!a1u!arVu!a%qwae`!a%n $ih`!bVaSr au!d _onVq

t = 20't = 60

'"ce"nt = 100

~

@(@ U


X[5*Y E[Y[ &([I*¨=()¨!dk-7'λ1

K=H7EI A C F A M wg[YH()*)*R7E C FH)**

λ1 C H)** ADC H* AA*A X[5* A*A lE[hH()*)*R7E C ?H(Pa]X?(* .E .-(';]E[

)E C w C &)*Ph C A C .N C E[H* A C F A E[57lE[H()*)*R7E C )*Ph C C &Z7E .-Z C X[5* A*AAW =()+H* A*A C F A*AA E[)* g X?(* .E .-(H()*)*R7E C w C &_ C E_HH(' C E[Y GE C +vE[YH()*)*R7E C Z C H C *YE[57j C X[5* A C F A*A E[YH()*)*R7E C )*)*R7E .-(.N H) Zk[)*j C X[5* A*A*A E[H()*)*R7E C ?IDk+ C ;X? C F .E')*jX?)' C .Y%HX .\l C FTHX .\l[5 C )*.N-7 C *[Fv ADC E C F C HIN vR)*&( 5)*Pa*X? C F©*Pa C IN C X?)g' C .HX .\¬E[5 C *Ph+5)*Pa &Z)*F C &E\ ;X? C F .E')* E[)*h ][ &([.N~X?(* .E .-(aH()*)*R7E C =()!H\[H*Y C 7|X[57EI ¨ij C *w' C E.N ;R)*&( 5)*Pa¨*X? C FWPa()*Pa C INa C E[5 C *Ph5)*Pa g[ Y * PaX.N?H'* ;X? C F .E')*X?)Y' C .Y%HX .\)*!-()NT*PhH(PaX5)*FuEE[aHX .\EGH\| WVH)"X57*E) C H C H) C C &E[_ C O ' C Ha+*)*H\[HIE .-G .E C E[QH()*)*R7E C ?IDk+ C E\ ;X? C F .E')*" C F 5)*P * ]H CC ? =(' C Fv g[)*R7E C *[ X ?IDkj C C FaX)* E¨ -G *'5 F_ C $ &(')*gU n g[*( F_ C *[<kYE[QX)* EY%E[5)*PaY C *H C F C &()*F) $5()E[5)*Pa ?E[QH()*)**X| C F C & ;X? C F .E')*©)* X*EF Yk[ H\[ =()*P H)*<kF X|( C E ADC X[5* A gE[F Z;¬)* C H"¨X)* E Pa C & 5)*Pa")*]-()N~ & C FuFH)** =)*(P X[5* A EX[5*A*A*A ;X| C F .E')*¨X|)%' C .%¬HX .\; C F_X)* E)* C &Z7E .-(.N]H()*)*R7EFv g[ ?H'*]R)*&( 5)*Pa C -(YPa()*"Pa C IN C C *(';E"-(('Pa5';YX|)' C .HX .\_*Ph 5)*P[5[ &([) ;X? C F .E')* ADC X[5* A*A K C F C E C F C HIN* C X[5* A*A*AM 5)*Pak .E[~E[_EPa_X)* E"[5-(_Pa()*Q-)* R . NT C E[ ) ;X? C F .E')* g[ jH C ?Y* C C E[Y)E C &Y ;X? C F .E')*+ C X[5* A*A k[ H\[ +E[ H)gE[5 C C X[5* A 5g[!EPa +- FW=()gX[5* A*A*A g["HI()*)EIR7E C HG<aH C Eg?IDk+ C ;X? C F .E')* C FX)* Eg)* *'PaPh)* F C QU n "$5()YH\[uX[5*¬E[ 5)* H('P C *[dkE[QH()*)*R7E C ?IDkj C E\ ;X? C F .E')* C F!X)* E ( C F"E[¨*H C FQH'P C *[dklE[¨H()*)*R7E C ?IDk+ C ;X? C F .E')*!X?)"' C ."jHX .\% C FuX)* E ADC X[5* A vE[)*_ "[5)*F.N~ C N)*R7E C *[ XT?IDkj C X?)' C .HX .\ C F~X)E\ C H* A C F A ?k[)*λ1 <k gg[]X?(* .E .-(!H()*)*R<\ . C C H)**=()H* A*A C F A*A*A

λ1 C H)** ADC

X[5* A*A C F A*A*A E[%H()*)*R7E C =)lH* C &Z7E .-( ADC X[5* AA E[H()*)*R7E C [ &([)=()<k -'

λ1k[)*Y[ &([

λ0*PaE C H)**jE[gH()*)*R7E C * &([ZE.N(

$5()[ &([)λ0 C F

λ1|E[]H()*)*R7E C FH)** K=H* A*A C F AA*AM ADC X[5* A*A*A |E[

@(@ ^


0 2000 4000−5

0

5

10

15

λ0=0.4, λ

1=0.2; t=20

0 2000 4000−5

0

5

10

15

λ0=0.4, λ

1=0.2; t=60

0 2000 4000 6000−5

0

5

10

15

λ0=0.4, λ

1=0.2; t=100

0 2000 4000−5

0

5

10

15

λ0=0.6, λ

1=0.4; t=20

0 2000 4000−5

0

5

10

15

λ0=0.6, λ

1=0.4; t=60

0 2000 4000 6000−5

0

5

10

15

λ0=0.6, λ

1=0.4; t=100

0 2000 4000−5

0

5

10

15

λ0=0.8, λ

1=0.6; t=20

0 2000 4000−5

0

5

10

15

λ0=0.8, λ

1=0.6; t=60

0 2000 4000 6000−5

0

5

10

15

λ0=0.8, λ

1=0.6; t=100

0 2000 4000−5

0

5

10

15

λ0=0.8, λ

1=0.2; t=20

0 2000 4000−5

0

5

10

15

λ0=0.8, λ

1=0.2; t=60

0 2000 4000 6000−5

0

5

10

15

λ0=0.8, λ

1=0.2; t=100

X)* E · · · 3 ;X? C F .E')* |X'H$ &(')*U n C F`%)* E

@(@


U n ¨ij()*)*R7E C ? kj C C FT`%)* E a`%[5*

b`%[5* A `%[5* A*A `%[5* AA*A

i+* E\ X'H E\ X'H \77 X'Hi+* A c eUZe( c c U(UZ c e @ @ c U @dn c c(c J c KJ c ^7Ui+* AA c e(eU n c @ UwJ c KJ(eUq c KJ7U(Uw^ c UZ((B c KJ(J @i+* AA*A c @ eZ c KJ @dc c U c ^ c c KJ7Uw n c K^ c UwJ c KJ(JeZ^i+* A c @ U c ^B c c;@dn c UZe(Uq c K^ c J7U c K^ n;@ B c @ (^

a"sbVa "u|q`Dk#_p Vflegd ega%ck|bgrVb"cqwaqwbV_#9qs`!bVak#_u!u!apmc`!d _e $ a#` zaae rVu!_ o`yq/ce"n `!bVaS`!_`|cp a10or ae"nod `!Vu!a%q;Y`!_`ycp7AB'ce"nl`!bVa1qwa%k#_e"nhqwbV_ 9q `!bVaIk#_u!u!apmc`!d _e $ a#` zaaejrVu!_ V`|qzce"n a10ortae"nod `!Vu!a%qsr au/VeVd `9_v kcrVd `|cp ;xrV"kAy~bb"cqwa%q$#B' # #B'Vce"n ###scu!a1u!arVu!a%qwa#e `!a%n $ ij`!bVaSrtau!d _VnVq

t = 20't = 60

'"ce"nt = 100

~

;¬HIE!H'*F ZN©E[_*)*H\[ C E C * .E λ0 C F

λ1-7 C *[v _g[_H()*)*R7E C )EIPh C

C &Z7E .-(!)*(' C FTJ c X?)H C =()?=(')gH* ¨g[ g .'E)E7EF C $ &(')* U n g[uHI()*)EIR7E C HG<aH C E?IDk+ C E\ ;X? C F .E')* C F X)* E*[<kF Z;¬)* C WX57*E) C [)*W C E[TH*© ;X| C F .E')*X?)h' C .h HX .\ C ;¬HI_

λ1[57 ? C FIEHIEF7 Q C X[5* A C F A*A C E[WH*E\

;X? C F .E')* λ0*PaQE©XRdN T(IN )*( ADC X[5* A E[WH()*)*R7E C =()][ &([

λ0K=H* A*A*A C F A M +P 'H\[dkj)+E[5 C C H* A C F A*A k .E[ )*R7E .-(.Na<kλ0 %VY

H()*)*R7E C Hw<aH C \ ¨X[5* A )*QX?(* .E .-( ADC X[5* AA C F A*A*A E[QH()*)*R7E C?H(Pa C &Z7E .-( ADC H C E)EhE X[5* A ¨ [ &([

λ0 h**wH R7EFk .E[ [ &([)

H()*)*R7E C C X[5* A*A V dkλ1*Pa_E C H)**E[H()*)*R7E C * &([ZE N( g[

I-G F C H© _H(PaXIE.N F Z;¬)* C h C X[57E AA*A j$()adkλ1E[H()*)*R7E C a)*E[

[ &([-K=H* A C F A M k[)* E[)*!*PagE_? C _ C O ' C H!λ0

.E[ )**X?HI]EE[hF'EPa C !X)*GH*] X?( H "!';\. C F C L%w'57E C Ke; K M C F Ke; M C X5&(h i¨[5X;E)]e lE[_F Z;¬)* C !)**'.E!H C H) C C &E[_HX .\EGH\] C F]E[+X)* E)* C *')*X)* * C & VYE[+F'EPa C 5E[ ;X? C F .E')*FX? C F C X)* E ¬E[INT*[('F©?QPa()*! C O ' C E RE[5 C E[QHX .\EwH| g[ - Fa7¨¨=()X[5* A*A C F AA*A wg[YHX .\5EwH [5j C C F )*HI¨ PaX5HI?H'*E[ X?( .HIN_ ¨Pa*')*FWX?)j' C .jHX .\ g[G' ;R)*&(5)*Pa¨*X? C F*¨Pa C INX?)"' C ."+HX .\E[5 C *Ph 5)*Pa l'; l C *(';E C 'P |)* R)*&( 5)*Pa '*'5.N*X? C FuPa()*]P_ C IN( A Y PaX?()\ C E C E]E[57YE[ C .NG* Y PaX .E[57 5)*P X?( HIN! E)* C &(.N]()* C EFQEdkg)*F\[+?[5-G (')%? .EX57E)* C C &HI'*E(P_)* A |E[

@(@


5)*PaY) C Y[<k3Eh?[5-Z¬X5)E H'R)*.N C X[5* A*A |E[)*] C &Z7E .-Z!H()*)*R7E C?IDk+I C X?)]' C .]gHX .\¨ C F X)* E % C F E[aH()*)*R7E C ?H(Pa][ &([)=()<k

λ1 g[ YPa C \[5<*'HH**='5)*PaY C -( *YPa C IN C X?)Y' C .Y

HX .\?E[5 C *+*'HH**=' 5)*Pa [ C E[ H'E(PaI)g5* +Pa)EY*H')*5 * ; .λ1 ¨dk 5)*Pa¨ C -Zj*jPa C INa C G';Ë[Y PaX)*d-ZPa C ¨vEH\[ C ((&NaX|)j' C .

Pa C IN*X? C |I*E)gE[5 C .λ1 g[ &([)

g[ ;X| C F .E')*"*PE?Q? C 5H R C E[ 5)*"Ph)*I X[5* C ()*F)E*H')* E[ )*I-( C ' Q$5() C Ik 5)*P C WPh)*I v . ** C E R7E[57" C Ik 5)*P C Ph)*IgH)*7E!QH'E(Pa)g5* g[)*I=()*E[ H()*)*R7E C |I kj C X?)g' C .+HX .\ C F X)* ! "X?(* .E .-(_ C E[ 5)*]X[5*W C F .! C H)**! C

λ1 hg[aHI

E[57E[ C &Z7E .-("H()*)*R7E C ?IDkj C, X?)' C .HX .\ C FX)* E?H(Pa[ &([)]k \[ TFH)** C &u*)*H\[ C E C * .DN gE[7HIE'5jH'E(Pa)* ] C &()*Pa C k .E[E["X)*I-G ('*.NWPa C E C F C F C & E[57 5)*Pa'*"E[ ) E)E7E&NX5** .-(.N( g[! C H C E .-( E_ CC d-7E ()g Pa .\<E g[ &([)g';*;¬HIE .-( =()[ .&([

λ1

!x<2¦¢y476=2?> ]2?I4<g[©FI-Z(XPa C W E[©X)*wF'HIE C H(Eh=()hF Z;¬)* C

λ0 C F

λ1 hX)** C EF C

$ &(')*WU @dc +[*(. F C W*[dk \[-Z)E&(X)*GF'HIE C H(E Ë[F5*[F¥ C C F H7EYE[ )E C &( X)*GF'HIE C EH\[ C w' | C FE[ F*EF C +H()*)**X? C FEQE[\ C F5)*FuFI-G R<\ . C "$5()H* vE[ X)*GF'H\ . C H(E FH)**_d-()E[QH(')** E Pa g[IN¥H C -()*&(EuE[ ) <kj)_|(' C F79E)a c n(c X?)* GF ¥V+_E[ C FE[_)*' C K

t = 100M vE[ )*F'HIE C ¨H(E" C F'HFuZN~ CC d-7E C C Fu Pa \7E . C [5

)*H\[F C )*.N_E[YEPaY.I-Z¨ C 5=(')¨H* C Pa.N c c(c ^(J K=H* AM c c(c ^(J K=H*A*AM c c(c ^7U K=H* AA*AM 5 C F c c(c ^ @ K=H* A M V++E[ C FE[ )*' C K

t = 100M ; C .Nh C

H* A E[)*]*PaEh?][5)*F.N C NF Z;¬)* C H] C X)*wF'HIE C H(E?IDkj C 5)*Pa ADC E[ H* A A*A 5 C F A*A*A ;E[F Z;¬)* C H"7+E[ C FXX?)*g &(&()¨=()+[ &([)+*)*H\[ C E C * .E I !g[ H(PaX5)* * C k .E[~H* A C F H7EYE[57E[_)E7EQjH C -()*&( C Ha [ &([)+=()g[ &([

λ1

g[I-Z¬jkj¬Ë[H)*(* D*HIE C ?X)EwF'HIE C H(E+H CC +?H)*.N_ ;XR C FwN©E[_HI C \IR7E C

λ0 C F

λ1 g[_*)*H[ C E C * . N©j?E[~E[_X?E C E RH C

*'Pa)* C F E[WHIE'5¨H'E(Pa)*]*P \T[5-Zh .*E._;¬HI C E[hFH)**+E[d-()E&(YX)*wF'HIE C H(E+.E[('&([aE[)*)*F Z;¬)* C H+|I kj C E[=(')¨H* g[Pa(¨(Z-G ('¨F Z;¬)* C H %E[Pad-(Pa C ¨¬E[Pa C P]'P C FhPh ; PQ'P V 'PaXa

@(@


0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

λ0=0.8, λ

1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &(')* U @dc %Vl-()E&(!`%)*GF'HIE C ij(E

@(@dn


E[jPa C PQ'P C F H7ElE[j'*+| C Ik EH\[ C ((&N k[)*% 'PaX]5E[jPh ; PQ'P gX)*(5.NWH'*FTZNE[" ; E[ 5)*P k .E[E["R)*&(X)*wF'HIE C H(E

]2?>¢¤ swx7

V C PaX?()\ C HIE() 5)*P *'HHE© E[ C 'P |)QH'E(Pa)*© 5)*P H C7*E)EHIj|H'*' C *(FaEGH\wjF Pa C .*[aX)* Ej C F wE[)*I=()*G P_ %E[X?(** NQ C H)** C &_E[]Ph)*IY*[5)* A E') C Y(';E[57E[! C .E vPa *Ph7EH\[%FIPh C F© C F*'XX.N_FH)**+<-()E[H(')**Y¬E Pa g[YPa(¨)EX Fh C Fh*'HH*='vF'EPa C \( XR7HW .gE[HIE .-(WH'E(Pa)* *)*H\[ k .E[ [ &([ C E C * .DN( ug[ Q Q)** C ?H'* E[_X)***')*_ C E[ * C &(5)*P Et;¬)&(GGF"7"dk X)* H [ &([) ]VYk ¬?"*[dk C R7E) 5_H C *w' C H 5E["5 C w)*'X;EHIN)E7E" * [ &([) $ &(')*U @(@ *[<k_E[ C 'PQ?)_H'E(Pa)*h C F¥E[TPa(' C a(';EX';a*()EF C*H C F C &h()*F) gg[57Y 5E[]*Ph.5)*PaY7)E" C E[!-()NI9Y C FE[!R)*&(Y CE[ )* &([Z "g[_ C !E[57 C ?(FT NGX|_)*X)** C E E[_Pa(' C ¨(';EX';"*'XX F C FE[!FE:K9k[ H[G(W *X ( M C F H7EE[!FPh C F©5)*PH C \["&( .-Z CX?)* GFv *'.E!)* &( .-( C =()E[ X?)* wF

t = 20t = 60

C Ft = 100

Qg[_*HF Z;¬)+E_ C E')* E[57gE["F .-()*&( C H"?IDkj C FPh C F C F*'XX.N)*Ph C +H(PaXIE ADC X[5* A C ;H*FPh C FWH C | (*)-(F=()j*Ph-5)*Pa C F C ;H**'XX.N=()¨R)*&( 5)EP_=()j5H* %g[ ¨F .-G * C (Z-G (' ADC X[5* AA wE[ ;H*gFPh C F=()a*Ph7 5)*Pa_-7 C *[W

λ1 C H)** $5()_dk

λ1K=H7EI A C F A M E[ ;H*

FPh C FW=()+*Ph!5)*Pa+)*Ph C ADC E[H* AA C F A*AA ;k[)*λ1 j)*R7E .-Z.N_[ &([

Pa(]jE[aR)*&(5)*Pa])*h E©F'!E[ )"(';EX';]EE[hFPh C F H C F .E C A λ1 dk KH* A C F A M R)*&( 5)*Pa_ kjg_*Ph 5)*Pa [5-(F Z<aH'.DN C

F'E C &~E[ )_(';EX'; ¥EE[57_E[)* _* u&()*7E) C 'PQ?)_ 5)*Pa_ C E[Ph)*(d %g[ +E C F C HIN?HI(PaYPa(gE)* C &()g C X[5* AA*A C H* A*A C F A*A*A GH7EI A C F A PaX NQE[57jPh C N5)*PaK=I-Z C *Ph)5)*Pa G C FX5)E H'R)* NPaF 'P D* F M H CC "F'YE[ )Y(';EX';YEWFPa C FuXX)*(X)* R7E N CX[5* A*A*A $5)EIHE C &FPh C F~?H(Pa Pa()*]F Z<aH'.=()Y[ &([)

λ1|H'*aHIE .-Z

H C *'Pa)* C &Z&( C E C * .-Z NQ C *)*H\[ C &"=() dkj)%X)* H g[F .-()*&( C H?IDk+ CFPh C F C F*'XX.Nh C |=(')+H*g C H)**+=)*(PX[5* A E X[5* AA ADC E[H*A*A C F AA*A |X[5* A*A*A <k[)*

λ1 )*R7E .-(.N"[ &([ 7Pa(E[ 5)*Pa)*+EF'

E[ )g(';EX';E_FPh C F 5';*(Pa"E["R)*&( 5)*Pag[5-(!F Z<aH'.E + C F( C &_*

@ J c


0 2000 4000 60000

50

100

150

λ0=0.4, λ

1=0.2; t=20

0 2000 4000 60000

100

200

300

λ0=0.4, λ

1=0.2; t=60

0 5000 100000

100

200

300

400

λ0=0.4, λ

1=0.2; t=100

0 2000 40000

50

100

150

200

250

λ0=0.6, λ

1=0.4; t=20

0 2000 40000

200

400

600

800

λ0=0.6, λ

1=0.4; t=60

0 2000 4000 60000

200

400

600

800

1000

λ0=0.6, λ

1=0.4; t=100

0 1000 2000 30000

100

200

300

400

λ0=0.8, λ

1=0.6; t=20

0 2000 40000

200

400

600

800

λ0=0.8, λ

1=0.6; t=60

0 2000 4000 60000

200

400

600

800

λ0=0.8, λ

1=0.6; t=100

0 2000 40000

50

100

150

λ0=0.8, λ

1=0.2; t=20

0 2000 4000 60000

100

200

300

400

λ0=0.8, λ

1=0.2; t=60

0 5000 100000

100

200

300

400

λ0=0.8, λ

1=0.2; t=100

FPh C F W · · · %*'XX.N$ &(')* U @(@ YPh C F C F©OG'XX.N

@ J @


)EF'5.N 5)*Pa) C [dk EhF'E[ )(';EX';E_E[ )FPh C FH C F .E C jg[ C H C E .-ZWE 7) C QE[*E)* C &(I) E[Pa()*X)* H7*E C E .-ZWE[ ) X57E)* C C &~H' E(Pa)*)* %g[57 C E[ 5)E C \ C H5 .g +Pa()* PaX|() C j=()+E[ 5)*Pa+E_XE[ )gH'E(Pa)*gE[5 C Ea7*E)EHI C Ik3 C

ADC FF .E C E $ &(')*jU @(@ E[g-Z)E&(+FPh C F_ C F *'XX.N] C E[gPh)*I% *[dk C C$ &(')*YU @ JG %g[ Ph()¨X57*E) C F *H'**FT?d-( +H C 5)*PaFv %g["*( FW C wk[ H\[*[<k_E[FPh C F 5)*a C H)**h C F¥ _?d-ZE[T-()E&(E'XX N K9E[F5*[F C M V9E)*(Pa X?)* wF E[")*R7E C *[ .XH\[5 C &(* E[57*'XX.N ;HIF5FPh C Fv YPh C F~ C FT*'XX.N)E'&([.N=(dk E[!DNGX H =DHINGH"X57*E) C C C F'E)N ADCE[ 5)* X[5*%FPh C F C H)** %?I=()*W|H(Pa C &©E7E R7EF C F FH)** C &u79E) kg7)EF OG'XX.NT)*HIE EFPh C F©k .E[ WH)\ C E Pa]R& ]ij C *w' C E.N C ;H*FPh C F +=(.dk+FwN C ;H*Y*'XX.N(

g[WX|( C ]+E Paa7!k[ H\[ E[h)*R7E C *[ .X ?IDkj C FPh C F C F *'XX.N H\[5 C &(FX? C F"* &([wE N C

λ1 A

λ1 )*R7E .-(.N[ &([ K=H* A*A C F A*A*AM ¬E[QE Pa]*X5 C

;H*YFPh C FREg C &()jE[5 C .λ1 g<k K=H* A C F A M

C d-()E&(?*'XX.N ;HF FPh C FT C v=(')H* Vl-Z)E&(]FPh C F©Pa(' C EE@ G Ke( @ K=H* AM ZJ7U Ke(( K=H* A*AM ZJ(JG @ (^(-K=H* A*AAM Z C FaJ c KJ(e( K=H* A M Vl-Z)E&(*'XX.N" J n @dc Z K=H* AM 7eU c (eZ^ K=H* A*AM 7eZ^G c;@dc e)K=H* A*AAM < C FQe(e; KU(U:K=H* A M g[a;¬HIE"

λ0 C F

λ1H CC "?_* .N©F E C &(' *[F~?H'*_E[_)E C F(P;¬HI

C F'HFZNλ0+kjv+E[;¬HI()* &( C 7E C &!=)*(P

λ1)*H C \ C F C E[ FPh C F

g*'XX ) C aH C [<kjI-() &('*"E[57!E[_)E C F(P ;¬HI] "F(Pa C C " C E[)*.NWX[5*k[ E["*)*H\[THIE .-G .E +E[!HIE'5H'E(Pa)*)* Pa()* C O ' C E R C R7E)gX[5*

g[ *PaE_H C 5)*P (*)-7E C C Ik3Ph)*IE 5k[I)E]79E)_X C )* C &_X[5*Pa()* C FuPa)E5)*Pa C E)E[ Ph)*I ?H'* E[)* ;H*!FPh C Fv !g[5)*Pa)* ¨R7E)lE[57E[+FPh C FQ[5FH)**F KHH()*F C &\E[+ .=HINGH+|YX)*GF'HI M C HZPa(/5)*Pa)*F'HjE[ )(';EX'; C FQ*(Pa¨E[P ; .E[jPh)*IhK=*[5+('; M ADC E[ * PQ'R7E . C )5)*PagE C FEh*[)* C |H'*]E[INk+)* C Y&( .-( C E[!X|(** .DNE)*'&(&( C &

@ J(J


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.8, λ

1=0.2

%FPh C F ;%%*'XX.N$ .&(')* U @ JG%Vl-()E&(IPh C FT C F©OG'XX.N

@ Je


:0:%< )I6ECP1R ECS D"I6EB0DEC@;F

g[_ C .NG* %E[QX)* HQF E)* ';E C ?E(&(IE[)Yk .E[TE[Q CC d-7E C X)*wH* C lE[Pa(+ C E)*E C & )**7)EH\[(1HIEgE[ * PQ'R7E . C A +k |?*[<k C E[57+E[d-()E&(]X)* H] C H)** C E[5)**Ph)*IX[5* .E[('&([TX)*GF'HIE C H(E)*Ph CH C \ C j()¨FH C g[ j ¨H'*FZN_E[YR)*&( C 'P |)jX|E C E R5H C *'Pa)*jE[57Ph 5)*PahH\[5)*&(T[ &([X)* H [ C H C *'Pa)*W?H(PaTE7E R7EFE[T* .E'57E CH[5 C &( g[*)*H\[HIE .-G . N HIE .-(H'E(Pa)*_F(Pa C 7EQE[ C O ' C H C E[X)* HI-(¬*QE[57 5)*Pa+H\[5)*&(dkj)jX)* Hjk[ C HIE .-(H'E(Pa)*+*)*H\[k .E[W[ &([ C E C * .DN( jg[]X)* H"F E)* ';E C gE[57Pa)*&(])*"E)* C &(.N*IkjF©E_E[])* &([Z C F)*"*[dk C Egk+¬E E["(& C ()*Ph?F E)* ';E C $ &(')*]U @ eh*[dkE[QHX .\ kj &([ZEF X -Z)E&(QX)* H K=*( FT C M |E[ )Y\ C F5)*FFI-G R7E C K=F*EF¥ C M C F E[Pa C P]'P C F Ph ; P 'P YH\[¥X?)* GFUKF57E[IF C M =()Y\[ F Z;¬)* C "H*!7j*)*H[ C E C * .E X g[_FI-Z(XPa C "Ë[_X)* H*PagE_|"* Pa )¨=()g?=(')gH* V3X)* H 'PaXH C ? * C 7gE[ ?&( CC C & X[5* A ADC E[ 5)*E[ )*F!;E[E PaE[¨X)* H)*¨)*R7E .-(.N[ &([] C F]FH)**j*dk.N79E)kg7)EF ÖG C HY C E[Y?&( CC C &Q])E C F(P;¬HIjE[)*('&([]R)*&( O <kX?E C E RH C *'Pa)*F(Pa C 7E 5)*Pa'*E[ l;¬HI% C F]H\[5)*&(¨[ &([!X)* H VYPh C N X?E C E RH C *'Pa)* [5-( |H(Pa HIE .-(QH'E(Pa)* ¬E[ HIE .-(QH'E(Pa)* C E[QPh)*I XRNWPa()*]FH * .-ZQ)*( ADC H C E)E EWE[QX?E C E RH C E'P_)* vE[Q*)*H\[ |[5d-G (')HIE'5lH'E(Pa)*Y C Y)E C F(P A Y ()* C EFEdk+)*FE[]X)* HE[ )*)* C FE[ )hH(PaX?IE .E()* ¨X)* H gk[ H[V;¬HIEWE[©X)* HT=()*Ph7E . C $ )*Pah[5-(u C C H C E .-ZWEuFH)**X)*wF'HIaX)* H C ()*F)QEuX¥E[ )QX57E)* C C &~H'E(Pa)* C F~E7*E)EHI C IkH C *'Pa)* Qg[ X)* H H(PaX|IE .E C ?HPa"[5)*F) *E[57E[FH)**!X)* HIgk vH C E C ' g[ [ &([)Ë[ )E C F(P;¬HIg&( C )E7EFZN

λ0GE[ [ &([)j Ë["-()E&( X)* H g[

H C ?T* C wN¥H(PaX5)* C & H* A Kλ0 = 0.4

λ1 = 0.2

M k .E[H* A Kλ0 = 0.8

λ1 = 0.2

M g[Wd-()E&(hX)* Ha=()"E[ak[(a)*' C @(@ c U c JW=()!H* A C F @ U K^(^7eZ^=()WH* A Q C E[~H C E)E)N E[~Pa()*© C E C * .-(©E[~*)*H[?[5-G (')]HIE .-ZH'E(Pa)* C E[QPh)*(I ¬E[Qdk+)Y YE[QX)* H "g[ H C ?Q* C wNTH(PaX5)* C &H* A*AA K

λ0 = 0.8λ1 = 0.6

M k .E[ H* A Kλ0 = 0.8

λ1 = 0.2

M _g[aX)* H_7"E[] "sbVa7rVu!dmk#a%qDcu!a ad b `!a%n $i`!bVa7fhcu!a#Ìqwb"cu!a%q/_v `!bVa "u!fhq/`!_ckk#_Ve`Dvx_u9`!bVa rVu!_rt_uw`!d _eg_vc

rVu!dmk#a1_e`!bVaS_#$au|cp p p a%$apN_vT`|boaSrVu!dmk#a~] !a^ noa#`|cd p a%nce"cp ioqwdmqz_v `!bVaSfl_flae`|q/_vT`|boaSrVu!dmk#anodmq`!u!d $Vo`!d _e"qsdmq d $aed e " c$Vp aX"~ #o~

@ J7U


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

λ0=0.8, λ

1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &(')* U @ e;%Vl-()E&(!`%)* H

@ J(^


C F¥E[)*' C Kt = 100

M U eZ7UZT=()QH* A*AA C FG c c(c =) H* A Q [ Cλ0 C F

λ1 C H)**]7E["EPa \ .PaE[")E C F(P ;¬HIY C O ' C HE[]-Z)E&!X)* H" C

X?)* GF *E[57 =() H* A AA l C F A*A*A E[_d-()E&( X)* H_ @(@ c U c J @ JG KJUZ C F@ U eZ n |)**X?HIE .-(.N( g[QX)* H]7YE[] C F~ ^G K^ @ K=H* AM ?U KeZ K=H* A*AM ¬ C FU eZ7UZ K=H* AA*AM (g[57% E[+FIE)*Pa C 7E C |E[+X)* H+ C HI)*\ C Ph)*I%FX? C F C

λ0+kj+ C

λ1 [ &([

λ0 C H)**+E["d-()E&( X)* H;k[)*Q[ &([

λ1[5

C &Z7E .-Z PaX5HIg C E[!-()E&("X)* H g[©\ C F5)*F FI-G R7E C E[TX)* HW aE[TR)*&()_E[©Pa()*T C E C * .-(TE[T*)*H\[?[5-G (')vH C *'Pa)* )K=?E[X?E C E R C FTHIE .-( M

λ1[5gE["Ph ()+ PaX5HI

C E[\ C F5)*F FI-G R7E C ©VY_$ &(')*hU @ eT*[<k %E[\ C F5)*F FI-G R7E C =()!E[F Z;¬)* C Ph)*IEH C ?¨)E C F H* A*A*A H* A*A H* A <g[j\ C F5)*F]FI-G R7E CvH* A %?IDkj C E[(*¬H* A C F A*A Zg[ ¨Pa C %E[57¨[IE)*(&( C I('jX)* H=()g[(Pa(&( C ('gX)*wF'HIEH C ? (*)-(FTPa()* .Nh C Ph)*Igk .E[[ &([*)*H\[ C E C * .E I K=<k*)*H\[ H(E M k .E[uE[a*)*H[ C E C * .DNujE[hHIE'5H'E(Pa)*! CX5)E H'R)%| C &!v PaX|()\ C H g[ *')*X)* * C & Z?H'*Y C gk+'Fa ;X?HIg"X)* HF E)* ';E C E[57 .gPa()* H C H C E)E7EFT C Ph)*(Igkg .E[[ &([*)*H\[ C E C * .E V C C H)**h C

λ0=()*H]E[W-()E&(hX)* Hh'X k[ H\[ k+7( C QE[h;¬HIQ

λ1 VY!E[

)E C F(P ;¬HIYF'!Eλ0 C H)** -5)*PaH C H\[5)*&(] C NX)* H"E[IN ( ?H'*!E[

C IkH C *'PaI)E)*+*%X)* Hg7*\ C E .-( VFF .E C . N ([ &([ X)* H O 'HIE'57E C C *'H\[Ph)*(\E"(X K7*E)EHI M H'E(Pa)**Pa%E!";¬HIE[-Z)E&(X)* H C &Z7E .-(.N C FE["F .-()*&( C H!X)* HX?(* .E .-(.N( $ &(')*U @ U*[<klE[¨PaX )* H(X)* HF E)* ';E C C -7)* ('lX?)* GF K9E[)*¨H('P C t = 20

t = 60

¬ C Ft = 100

M C FT=()E[QF Z;¬)* C H C ER7E C λ0 C F

λ1K9=(')

)*<k M ©g[WHX .\kj &([ZEF X)* HhF C * .DN =()!E[WF Z;¬)* C ]-']λ0 C F

λ1

&( .-( C =()E[?&( CC C & (E[Pa FF.g C F_E[ C Fh?E[* PQ'R7E . C )*' C %+[ C 'P |)-)* RY C H'FF~ C \[QF C * .E ")*Q?IDkj C J @ ZJW C F c;@dn "g[ )*X?()EF C ] @ C VYXX? C F 5Xv @dn JG VYgX)* HF E)* ';E C _7)EE)* C &(.N *IkjFE~E[)* &([Z $5()_+H C ER7E C λ0 C F

λ1\[uX)* HuF E)* ';E C )*u|H(Pa C & Pa()*~H C H C E)E7EF K= * g[5-(

[ &([)X? C F©_<kj)\ C F5)*FTFI-G R7E CM E[! C &()gE[!Ph)*I ; E K= * E[R)*&()

t M A h k+()E[Zk[ C E C &uE[57aE[©NGPaPaIE)N E +)*Ph C _F*X .ET

E[_H C H C E)E7E C [ Ct?H(Pa"R)*&() &( .-( C

λ0 C F

λ1K9=)*(PE[ @ !H('P C

EE[ae)*FuH('P CM vE[_X)* H_F E)* ';E C Pad-ZQEE[_I9 g[ "Pa C E[57 E[

@ J


0 20 400

0.1

0.2

0.3

0.4

λ0=0.4; λ

1=0.2; t=20

0 20 400

0.1

0.2

0.3

0.4

λ0=0.4; λ

1=0.2; t=60

0 20 400

0.1

0.2

0.3

0.4

λ0=0.4; λ

1=0.2; t=100

0 20 400

0.1

0.2

0.3

0.4

λ0=0.6; λ

1=0.4; t=20

0 20 400

0.1

0.2

0.3

0.4

λ0=0.6; λ

1=0.4; t=60

0 20 400

0.1

0.2

0.3

0.4

λ0=0.6; λ

1=0.4; t=100

0 20 400

0.1

0.2

0.3

0.4

λ0=0.8; λ

1=0.6; t=20

0 20 400

0.1

0.2

0.3

0.4

λ0=0.8; λ

1=0.6; t=60

0 20 400

0.1

0.2

0.3

0.4

λ0=0.8; λ

1=0.6; t=100

0 20 400

0.1

0.2

0.3

0.4

λ0=0.8; λ

1=0.2; t=20

0 20 400

0.1

0.2

0.3

0.4

λ0=0.8; λ

1=0.2; t=60

0 20 400

0.1

0.2

0.3

0.4

λ0=0.8; λ

1=0.2; t=100

$ &(')* U @ U`%)* HY E)* ';E C

@ J(


X)***')*]Eadkj)X)* Hk .wHH') ij(PaX5)* C & E["=('))*dk ? C !H C (*)-Z!E[57 C E[ 5)*jDk+QX[5*g C C H)**F

λ1 C -((.-ZE[X|aFH)** C & %g[;¬HI+E[57

E[QPaF R C C F©E[ C 'P |)Y(';E )* C E[])* &([ZY* F] C H)** YH'*F~ZNE[ C H)** C

λ0 g[ ¨;¬HI¨kj( C j C X[5* A*A ADC X[5* A*A*A

λ0 C H)**¨E[PaF R C

C .N¥* &([ZE.Ng C Fλ1V;¬HIEhE[©X|¥ C .N¥ C E[kgN \[5<W .hPa<-(aE E[TI9

C aH C H C H'F_E[57!E[a C H)**F *)*H[ C E C * .DN~HIE .-(aHI C *'Pa)*>Kλ1M =()

C E[)%*'XX )k[!*H\[X?) wFG C )**'. C \)* C &)X)***')*gE"FH)**E[!X)* H"X?)* g$ )*% X)* H?H(Pa!Pa()*"F *X|)**F© .

λ1 C H)** OGH C F

k[ Cλ0?H(PaaR)*&() j&( .-( C

λ1 5)*Pa E C FE H\[5)*&([ &([)aX)* Ha?H7'ET

E[])E C F(Pa.NPh7EH[FTH C *'Pa)* C .N C E[!E[ )*FTX[5*?E[]X)* H!F E)* ';E C F C H\[5 C &(Q)*Ph)*7.N .

λ0 Y C H)**Fv "j';E[)*vW[ &([I)Y*)*H[uHIE .-G .DN

HIE'5H'E(Pa)* C H)**gE["X)* H"H(PaX|IE .E C ADC E[ .E)E7E')* . QPa(E.NuE[(& C ()*Ph¨ C F E[`)*IEuF E)* ';E C E[57_)*X)*(X?(*Fa%X?(** +F E)* ';E C =()X)* H% C F5)*P D* X _E%E[g[wNGX|E[* k[IE[)!E[_X)* H_F E)* ';E C ]`)*IEF E)* ';E C ¬E[ (Pa(&()*d-ZOGPa .) C d-&(GGF C * DR gE XX Fv g[ C 'v[ZNGX?E[* +=()*PQ'R7EF X

H0 : Xi ∼ F0(·),

k[)*F0(·)

C NH'PQ'R7EFF E)* ';E C =' C HIE C E[57 gH(PaXIE.NhEX|H 5F© C FH C \ C '(' )*

F0(x) =∫ x

−∞1√2πe−

12xdx

=()E[¨(&Z)* .E[P_ F!X)* H;E[¨(& C () Ph?F E)* ';E C C F

F0(x) = 1− (x0/x)aI(x0,∞)(x)

=()¨E[I-(¬X)E .Hg7lE[ `)*IEF E)* ';E C g[_Ph ; PQ'P .[GwF©E Ph7EE[ X5)EPaIE)*Y=() `)*IEF E)* ';EF)E C FP -)* Rg)*"&( .-( C X

x0 = min1<i<n

Xi

C F

a = n

[

n∑

i=1

ln(Xi/x0)

]−1

.

] [#aa1a~("~JH \98J8F1 2 ;=>*>0O&Ace"nCE1/%5Na#`Dcp ~F;=>*>@G*Ay~] f aa1a~("~ 11 )a#`Dcp ~F;=>0O#XD'r~IG.*?@Ay~] #aa1a~("~ + 572F2F+ ;=>*>0O0'rVr~.XD%X0Ay~

@ J


C F)gE[ C 'v[ZNGX?E[* \[EY\7E E H

Kn(X1, . . . , Xj, . . . , Xn) =√n sup

−∞<x<∞|Fn(x)− F |

|E[ (Pa(&(()*d-ZOGP_ .) C d-!&(wGF C * DR E NGPaX;EE H N]XX)* ; Ph7E.N"F E)* ';EFh

[1−2∑∞

j=1(−1)j−1e−2j2x2

]I(0,∞)(x) ij)* .E H;-7'%=() C .EEPaX)*

\Fv X h$5()E[ ¨H*;E[YH)* .E H-'7Ë[ n ^ * & C 5H C HYI-(? 1.3581/

√n

k[)*n E[ C 'PQ?)¨vE[YH()*)**X? C F C &Q)E C F(P-)* RK=EPaX* M =()¨7H[

H*]g&( .-Z C C ] @ C VYXX| C F 5X5&( @dn JG YU @dc E[dkg*(PaY\7E E H+ C FWE[YEg)**'.E+lE[PaX )* H5X)* HF E)* 'GE C =()E[_(& C ()*Ph7F E)* ';E C Qg[aP_ C -7'"jX[5* A H C |_)\ C (F H* AA*A Ke; c e(eZJ M H* A K JG n(c U M H* A*A K JG ZJ(J( M H* A K JG K^((e M Qg[ " F' EE[_)E C F(P;¬HI!wN©E[ *)*H[ HIE .-G .DN©Ë[ X?E C E RH C *'Pa)*

λ0l

F *H'**FT?d-Z ADC X[5* AA GE[ F Z;¬)* C HlE[ Pa C -'Pa C &]E[ Ph)*IE- C *[v "g[ Y?H'*_%E[ *)*H\[u;¬HI"ZNTE[ HIE .-(QH C *'Pa)*

λ1¬E[57 C .N

FH)**QE[aX?u+E[aF C * . N( ADC X[5* AA*A -()E&(hX)* H])*h)E C F ]H*A K @ ((( M H* A K @ Uw( M H* A*A K @ (e( @VM H* A*A*A K @ KJ @ M VY* X5)E.NF *H'**F¥?d-(E[W()*F)]gE[W\ C F5)*F FI-G R7E C ]H C \ C Q=)*(P X[5* A E X[5* A*AA C P_.NH* A*AA H* AA H* A H* A |F*X .E!E[!H\[5 C &(YE[()*F)E[!-()E&("X)* H g[ )**'.EE[(Pa(&(()*d-ZOGP_ .) C d-&(wGF C * DR E *[<k E[57E[ C '[ZNZX?E[* ¨h(& C ()*Ph7lF E)* ';E C %E[QX)* HH C | HHX;EF~=()Pa(lE[W)*X?()EF H* ~g[W C .N ;HX;E C ]k[)*WE[hE \7E E H K !O M ;HF_ .EH)* .E H¬-' K=HI- M )* E[5)* kjhX[5*YH* A*A*A 5k[)*]?E[*)*H\[© C E C * .E )*"[ &([v +U @(@ *[dk%E[+E Ph7E5E[gF E)* ';E C X5)EPaIE)*5E[`)*IE F E)* 'GE C C F©E[Q)**'.E %E[ (Pa&(()*d-ZOGP_ ) C <-&(GwF C *D7R E ADC E)*E C &(.N E[hX5)EP_IE)!jE[hdkj)!|(' C F jE[h`)*IETF E)* ';E C

x0[5!E[a*Ph

-'j=()Ë[X[5* A C F A*A H* A*A*A G=()¨k[ H[WE[ C '¬[ZNGX?E[* gl(& C ()*Ph7F E)* ';E C [5FuE?a)* HIEFv ADC X[5* A lH* AA*A [5 E[a*Ph."dk+) ?(' C FK JG K^7Uw7U M Pa C &wH* w.E[('&([!E[g-()E&(+X)* Hj|H* AA*A C X[5* A lE[+[ &([G V+gE[ EP_E PawE[ X5)EPaIE)+l\ |E[ H\ C *lE["`)*IE_F E)* ';E C

a

] #aa1a~("~ + 572F2F+ ;=>*>0O0'rVr~IG&>@G*Ay~

@ J n

U e; OG PQ'R7* C *'.E

A

RF PACJ1B

! " # $ !%

a

# b

# & # & & # & & &

'

' & ( )* +, ( - + ( ( , ( , . ( ( . ( ., + - - , , . . + (

' & & ( * ( ( - , ) . ( ( ) ( ( , . ) ( + , * , * ( *

' & & & , , , ( , , * ( - ( . ( ) ( , * , * ( ( . (* * )* + ( . )

' &/ ( . + ( ) . , ( ( ( +, (* ( - + . . * * +* (* ( + )

a 0 12 34 56 78 9: ; 7 : 7< : < : 4 : =< : =>@? >A 2 BC =: => 4 5A 4 56 7 4 : DE F < =GH = I> 4H > 7 5 7A 7 5?

b

J ; 4 < 7< KML KKML 4H N K K K 4 C 7 C 7O C 7< 7H : 7 NP Q : ; 7 O 7C =8 N< t = 20L t = 60L 4H N

t = 100?

! " # $ !

a

# b

# & # & & # & & &

' x0

x0 x0

' & - )* )* ( ( ( - ( , ) , * - , . ( , ., ( ( . , ( ( + ) ) ) + (

' & & - - - + ) ) , * , ( ) (* + ( * ( ( + . ) . + - .* ( *

' & & & ( ) - - + + ( , , . ( . + - + .* ( ) + ( ( . * . - ) , . )

' &/ . +* . ) ) ) ( ( ( - . ) . - . . . ( . , . ( , . , * + )

ax0

2 R =H =S 6 S 8 9: ; 7 < 4 S O 5 7A 4 56 7? 4 2 T 4 = 5 O 4 C 4 S 7: 7C? 0 1 2 34 56 7 8 9: ; 7 : 7< : < : 4 : =< : =>@? > A 2 BC =: = > 4 5A 4 56 7 4 : DE F < =GH = I> 4H > 7 5 7A 7 5?

b J ; 4 < 7< KML KKML 4H N K K K 4 C 7 C 7O C 7< 7H : 7 NP Q : ; 7 O 7C =8 N< t = 20L t = 60L 4H N

t = 100?@ ec


=()jH* AA*A ;X[5* A G Ë[Y*Phj C Pa C &Q.?H* ¨+[ +Pa C Ë[57jE[\ | )*R7E .-(.N]E[ H\ C F (E[)*I=()*wE[57%E[F E)* ';E C [5Ph C NQ(';E )* Z * E[)*)*Ph C N5)*PaE[57t;¬)Ya-()NT[ &([©X)* H g[ YX[ C (Pa C C E[dk h[ &([TX)* H][I)*(&( C .DNW C ]Ph)*(Ijk .E[[ &([

λ0 C F

λ1 %g[ )**'.g\[ (Pa(&()*d-ZOGPa .) C d-

&(GGF C * DR +E*[<kgE[57gE[ C 'v[ZNGX?E[* `)*IEaF E)* ';E C H CC ?HHX;EF~=()YPa(Y%E[QH* "L ;HX;E C )*]X[5* AA H* A*A C F~X[5* AA*A H* A*A*A wg[ )**'.¨ C j*')*X)* * C &" .¬ C Gw¨7E[PaX )* HF C * .E C $ &(')*U @ U g[*Ph C 'PQ?)jX)* HjE[57+)*YI9j C E[I9jvE[PawFYvE[F C * .DN C F H7EE[57E[F E)* ';E C %Pa()*g .NQ"(& C ()*Ph7GE[5 C "`)*IE"F E)* ';E C !U @ J *'PaPh)* I*(Pa!\7E E HE[!PaX )* HvI-(lX)* H g$5()H C E R7E C j

λ0 C F

λ1;E["d-()E&( X)* H[5-( E[ ()*F)X[5* A X[5* AA X[5*

A*A*A ;g[EPaY ¨- Fa=()E[\ C F5)*FFI-G R7E C g[ *Ik C E C FhE[w')E(* +FC g=(dk H)g()*F) ËE[57E[ *(Ik C EY C FE["w')E(* )* -()N* C * .E .-(E_(';E )* C F ;E[)*I=()*5=Ik (';E )*+[5-Z! FH * .-(" C O ' C H! C E[ )+-'

U @ JGÖw\7E E H+E[!L%P_X )* Hv`%)* HY E)* ';E CS (Pa C E

i+* `%[5*a

Pa C EF *Ik C * w')E(* i+* A `%[5* A @ e; ZJZ^ U KJ7Uw n @ K @(@ ; n;@dc U

`%[5* AA @(@ KJ @dc e; @ Z(^ e; ((( e(e; U(UwJ @`%[5* AA*A ^G Uw^( c @ K(^( @ U c(n @ JG @ Z7U

i+* AA `%[5* A @ G Z^(f^G K^Z^ c c Ze( JG K( c `%[5* AA @ e; @dc e(U KJ c;@ U @ c ^ @ e ^G @(@ ^`%[5* AA*A U K^(^ c JG K(ZJ JG KJZ( n ((eZ^

i+* AA*A `%[5* A J @ K(ê @ ; n;@ (e @ c @ U c ^ n ^`%[5* AA @ e; e n ZJ U ZJ @dc c @dc J(J JG n J(^ c`%[5* AA*A U e(e(eZJ JG n Z^ @ KZJ(J ^G K( c

i+* A `%[5* A @dn c n ^; eUw^(J G e(Z^(^ e; KJ(J n J`%[5* AA @ U KêZ7UG c n n KJeUw @dc ; KJ @ @`%[5* AA*A ; n;@ (J e; KJ @ U @ JG c(c U J7UZ; e c;@

ab"cqwa%q!#B' ##B'ceVn# ##Dcu!a7u!arVu!a%qwae `!a%n $ ig`!bValrtau!d _onVq

t = 20't = 60

'ce"nt = 100

~

@ e @


g[57"X)* HFH)**_ C -()E&( C F'HFuZNTE[ CC d-77E .-ZQHIE .-G . NE[ 5)*Pa g[_FH)**_E[_\ C F5)*FuFI-G R7E C R)*&()Y=)*(P X[5* A EX[5* AA E[5 C =()E[ E)E C * .E C =)*(P X[5* A*A EX[5* A*A*A v ;HX;"=() H* A*A*A vg[G' E[ F *X?)** C%X)* HY|H(PaY*Ph)7a[ &([))E7E! C E[]RYX[57E]E[])*' C ADC H* A*A*A k[)*]E[QX)* H]F *X|)*E . C FH)**E) C E[5)* X|)* GF ?E[]X)***')* C E[X)* HF'E"[ &([_*)*H\[h C \ C E \ .%v|E[aH C *'Pa)% NGX|ËIPaE!|[ .&([)%=)*(PE[?&( CC C & g[FH)**Y7¬E[X)* HgF *X?)** C ¨7*!";¬HIEFhZN_"dkj)%?(' C FE[ X)*GF'HIE C H(E ¨g[ gH C * ? (*)-ZF C $ &(')*U @ e Gk[)*" C H* AA*AE["dk+)g?(' C F g)*H\[F C 5)*vH* ]E'P'X wE[ C .NG* vE[YX)* HIYF E)* ';E C *[<kË[57Ë[Y*)*H\[HIE .-G .E E[] kjH C *'Pa)&()*('X ¬E[QX?E C E RH C *'Pa)*" C F©E[ HIE'5H'E(Pa)* v[5-Z!F Z;¬)* C j;¬HI+ C E[I-Z¬ C FaE[-7)E C HYvE[YX)* H ADC E[Y*[()+)*' C ;![ &([*)*H[© C E C * .DNE[]X|E C E RH C *'Pa)*

λ0¬";¬HIEE[]d-()E&(]X)* H!X|(* .E .-Z.N

g[hPa()*a 5)*P ;X?HIEQ)E C F(Pa.N©Ph7EH\[F H'E(Pa)* E[a[ &([)! .! .E" C H C E .-(E_H\[5)*&(!Q[ &([X)* H C .NW X?E C E RvH C *'Pa)g +k . C &QE X5dN C NX)* H |<k[ )**)-7E C X)* H +V C HIE .-Z!H'E(Pa) k C & C *g\aX5N E)* HIE.N<kj)gE[5 C[ j)**)-77E C X)* H ADC E[Y C &])*' C ; .¨ ¨ PaX?()\ C =() 5)*PaË]Ph C \ C ]5*YH'E(Pa)* VYE[ )*)*H\[_ C E C * .DN

λ1( C H)** (E[+X)E5 .DN E[57E[IN!k G';N

E[ C GgX?)* GFa=)*(PQHI(PaX?IE .E()j*Q C H)** g[)*I=()*5][ &([W*)*H\[ C E C * .DN%E[ HIE'5H'E(Pa)*Yk lH(PaX|lE[5)*PaEWdk+I)YX)* H VY hH C *w' C H_E[ H(PaX?IE .E C E[-Z)E&(X)* H~Ph)*I k .E[ [ &([ *)*H[¥ C E C * .DN E[HIE'5%H'E(Pa)*

λ1k |adk+I) E[5 C C Ph)*I"k[)*

λ1 "dk" ADC ()*F) E

I-'57E X|( HIN© C E)*'Pa C E . PaX|()\ C YE[57 E[QE PaQ[()* C C F~E[ \7E_FI-ZI(XPa C "E[ )**X?HIE .-(_ C F'E)N~| \ C C EWH C * F)E7E C !VX?( HINE[57 Pa7 PaX)*d-G C & E[!H C *'Pa)* ? C dkF&(Q|('; 5)*Pa |X)* HPhN* .N[5-(QH C \)E)NW;¬HIY . . XX F7gE[ k)* C &aX|( C g\ .Pa

:0: GJI;R1D D"I6BHP DBI6R

ADC E[ *'*HIE C GH\[5)EHIE)* E H¬E[ C F'E)N G*'H\[WE[ C 'PQ?) 5)*Pa C E[ C F'E)N )E7Eg C E)N C F ; . ;E[ .=IE .PaY/5)*Pa ;E[ * F E)* ';E C 5)*Pa E[F&()*NGPaPaIE)* Pa C & 5)*Pa 7H C HI C E)E7E C C F H 7 C F"\ .DNYPa*')*=()Ph)*(I¨*[5)*+)*F.k .E[v OGI-()E?Pa*')*+)*XX F_E] C .NG*E[PhH)*X57*E) C E[57Pa)*&( C F(&( C ('*.N_ C F E[57)**'.E%=)*(P E[Pa H)* ?[5-G (')%?E[

@ eZJ


&( C E]HIE C & C E[a(*)-(F H C (Pa H_' C .!"F C F wN©E[aPawF%w'57E C " Cij[5X;E)YeG g[aPh() F x;¬)* C Ha?IDk+ C E[5)*P H\[5)EHIE)* E H! C F E[_Ph)*(I!E)*'HIE')*a E[57WE[~;¬HIE"E[©H C *'Pa)* gHIE .-G .E hH\[5 C &(~)*Ph)*<.N( ij C H) C C & E[Ph)*( E)*'HIE')*%E[HIE'5¨H'E(Pa)*_)* C dkPa(Q C O ' C E R C F C ;¬HI_X?E C E R(H C *'Pa)*lH C C .N|FIEHIEF] C E[*[()l)*' C g[ k+)*F;N(*)-(F=()+E["X)* H"F E)* ';E C V C C H)**a C E[h*)*H\[ C E C * .DNugHIE'5H'E(Pa)*

λ1H7'EI]E[aX)* HaH(P

X?IE .E C E_ C H)** * E[57gE[ X)*(5 N_E_*')-G .-( =() 5)*PagH\[5)*&( C & [ &([X)* HFH C g[ 5 C w)*'X;EHIN©)E7E] Y[ &([) C F ?E[)*I=()*¬E[ C 'PQ?)Y 5)*PaY C E[Ph)*(¨ dkj) g[ C H C E .-(gE! C E)E[Ph)*I¨ ¨*"dkj)*"E[57=Ikj)¨ C E)* GHH')" C Ph)*I"k[)*aHIE'5%H'E(Pa)*"*)*H\[ k .E[u[ &([u C E C * . N VY]H C *w' C H?E[]H C H C E)E7E C 5)*Pa |Pa*')*F©Y) C F5[ C F ? [ &([) ADC E[*[()")*' C ¬E[)* W[ &([©E')*' C H C Ph7)EI *[5)*E[57 C H)**" C

λ1 ADC E[

C &~)*' C %E[*E')*' C HIaF P_ C .*[ C F E[5)*Pa X E[ ) \ *[F Ph)*(I*[5)* ©I-()E[* 5)*Pa])*Ph C [IE)*(&( C (' C F E[hF E)* ';E C 5)*Pa! *[<k C E =(dkE["(& C ()*Ph7

¢¤,(%swxh2|z "g6=x7¤

$ &(')*U @ ^"*[dkjE[-()E&( C 'PQ?)¨ 5)*PagK=E Fa C M ZE[YPa C .Pa" C FWPh ; PhK=F5*[F C M + C F¥E[\ C F5)*FFI-G R7E C K=F*EF. C M V9E)a C H)** C &u=)h*[()E Pa|E[ C 'PQ?) 5)*PaYFH)**"F)EE H.N g[ ;¬HI YHF©*[5('; C F_[5%? C (*)-(F w=() C \ C HZ C E[';E(Pa( .j C F'E)NQZN ?H9B9F PS C F P/P ?H F K @dn (^ M V9E)k+)*F E[ C 'PQ?)! 5)*Pa! C H)** C Ik" T$5)*(PH* A EuH* A*A*A E[d-()E&( C 'P |)_ 5)*Pa FH)**aE ^ c K=H* AM U c K^K=H* A*AM e(e; K K=H* A*A*AM +[!-()E&( H* A 3 +UZ; @ %g[ 5)*g;¬HIE C 7\ E[57+k .E[W C H)** C &

λ1GE[ C 'P |)+ 5)*Pa+FHI)E* ¨g[ j +*]- Fa=()¨=()¨E[

C C 'PQ?)g)*Ph C C &5)*Pa ;k[ H\[ c K=H* AM ^5K=H* A*AM UZ K=H* AA*AM .E[©_-'!Z ?H* A ?IDk+ C H* A C F©H* A*A ¬dkjI-Z) ¬H(PaX5)* C &_E[)*R7E .-(] C H)**Q C E[ C 'PQ?)Y 5)*Pa=)*(P E[ |&( CC C &W' C E lE[Q C F ¬E[ )E7E"sbVaDeVf-$taus_v q`|cuw`!d e. "u!fhqzd e a%ck!b fhcu!a#`su!a%qwop `!d e.vxu!_fG`!bVa1qwbV_uw`skcp d $Vu|c`!d _e qwd fVpmc`!d _e dmq

X@?4;Zkcqwa #(AB'.X0 ; k#cqwa # #(AB'D . ;Zkcqwa # ##(AB'"ce"n &X;Zkcqwa #Ay~

@ e(e


0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

λ0=0.8, λ

1=0.2

%Pa C G%Pa C 7Pa · · · %EF$ &(')* U @ ^G%Vl-()E&(!'P |)$ )*Pa

@ eU


C H)**Pa(' C E!E @ Uw^ K=H* AM @ eU K=H* A*AM @ ZJ K=H* A*A*AM C F @dn(n K=H* A M vg[)*I=()* C H CC H C H'FQE[57" C C H)** C E[ C 'P |) 5)*Pa C ]H)\ C Ph7)EI+ jPa()*()j*+X)*(5E[5 C C E[)+Pa)*(IE A +H C ;[dk+I-() ? C EFWE[57+\[)*R7E .-( C H)** C E[ C 'PQ?)+/5)*Pa+ +R)*&(g C H* A*A*A C FA =()g[ &([-7'E["*)*H[ C E C * . NWE["X?E C E RvH C *'Pa)*

λ0

g[hPh () FIE)*Pa C C !jE[ C 'PQ?)" 5)*Pa!XX?)*"E?_E[a*)*H\[ C E C * .DNE[QHIE'5H'E(Pa)*

λ1|k[)*YE[QHIE .-G .E E[]X?E C E RlH C *'Pa)*Y[5-Z

.*E.;¬HI g[ W a C C j=()h C \ C H+k .E[E[ C F C &(aE[57h=()h[ .&([λ1E[

d-()E&(!X)* H)*!dkj)Y C F ¬k ?!FPa C E)E7EF |E[]X)*(5 DNWEh*')-G .-(] dk+)g .lE[)*" [5)*FH(PaX?IE .E C C X)* H

¨6=zsZ4<6¤ s2|z "g6=x7¤ ADC E[u)*.N\&(u!E[uPh)*IE[u C H)**u C E[ C 'PQ?)5)*Pa )EX F.N=(dkjFwN *[5D('; * R)*&(©k+d-( Q ; \Pa C E C F |<-( VYTH C *w' C HE[(* 5)*Pa¨E[57+ C E)jE[Ph)*Ig7g]R7E)¨X?( C jE Pa[5-( ]<kj))* *©j5 C w)*'X;EHIN( hVgFF .E C . N . "*[dk C E[57 E[aF;- C \&(_+.<kj) )* *© HH(PaX5 C FZNWE["F EF;- C \&(" dk+)gX|)=()*Ph C H5 * ;=Ikj)X)* E g[ .=IE .Paj-5)*Pa% FGH'Pa C EFa C $ &(')*+U @ Y=()* C &(+)*' C ¬H* A K

λ0 = 0.4 C Fλ1 = 0.2

M _g[ PaX_*[dk]W NGX HX57*E) C C E[_[()* C \ ; E[C 'PQ?I)h X?)* wFh _*[<k C C F C E[-()E H ; _E[ C 'P |)h 5)*Pa g[ &([Z%&()*IN_ C % C F H7EjE[ ; E C Hv 5)*P (E[F5)*Q&()*IN C E[ C C D ; E C H?I=()*_ C E)N K= C ?&( CC C &W=)*(PE[_I9 M () E[ E Pa 79E)"X)*I-G ('*.N© ; E C &5)*P[5FE_ ; .gE["Ph)*(I:K=\)E C &_79E) &([Zg&()*IN C M ADC E[ PaX¬E[ &([ZY&()*IN© C C E[Q<kj)I9 *[dk E[57E[ C F'E)N©\)Ek .E[uU n 5)*Pa ADC X|)* GF J vE[)*5)*Pa [5-Z E ; . E[ Ph)*(I Qg[ H C |_* CwNhE[" &[w+&()*INW C gH\[5 C &( C &QE[ )gH((')jE_H| %g["E[)g ; .EgPh C .NaGHH')?IDk+I C X?)* GF @dc C Fe c g[)*79E) .j ¨E[* 5)*Pa¨k[(*X)*(5 NQEQ*')-G .-Z C )*.N @ E[57Q .E[)Q[5-ZW*')-G .-(F ' C E ¨X?)* wF U c ()] C E)*F E[WPh)*I_79E)t = 30

+g[5)* 5)*P C E)*E[!Ph)*I C X?)* GFt = 3

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M

V FI\ FT C .NG* )*' C Y &( .-( C C !U @ e k[)*]E[!Pa C C FT\ C F5)*FFI-G R7E C E[ -Z)E&(Q .=IE .Pa!E[5)*Pa )*Q)*X?()EFv ]7\]E[57E[Q .=IE .Pa 5)*Pa H CC !?_* PaX.N©H(PaX5)*F E[IN )* hOG C H_E[_ .=IE .P_ 7g 5)*PE[57 C E)*E["Ph)*I =()g C \ C H| C X|)* GF

t = 90H C Ph ; Ph. NWPa(' C gE @dc X|)*

GF ;E[")**'.E+kj('F|"F E()EF C E[ k+NWE[57 5)*Pa+E[57 C E)7 7E)+X?( C %E Pa kj('F©[5-Z!E[Qdkj*')-G .-X)*(5 E . ADC ()*F)EW*]k[IE[)YE[)* _* & C 5H C F Z;¬)* C H! .=IE .Pa?IDk+ C 5)*Pagk[ H\[T C E)*FTE[!Ph)*I C E[ C .E R7GX?)* wF K= C H'P | C E M C F E[(* 5)*PaE[57% C E)*F_E[gPh)*I7¨R7E)X|)* GFK= C E)E C E M E["Ph ; PQ'P)*Ph C C & =IE P_[5gE_| \ C C E H C * F)E7E C C *')*hW )H(PaX5)* * C ?IDkj C E[_ ;X?HIEF .=IE P_Q¨E[Q kj&()*('X K= C H'P ? C E] C F C E)E C E M lE[_F57\k[ H\[ )*_'*F )*aF'EF =(.dk hij C H) C C & C E)E C E ( C .N!E[(* 5)*Pa)*+'*FQk[ H[Q[5d-(jE[+X?(** DN"?*')-G .-G C &Y=()7

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E[h C HI'P | C 5)*Pa E[aPh ; PQ'PE Pa g*')-G .-7 !?(' C FF ZN ^ c X|)* GF"=()H\[ 5)*P ADC E[ k+N ? . C *')*FTE[57Y C .NWE[(*5)*Pa)*!H C * F)*FTk[ H\[©)*H C =)* C \IF wN!E[+EPajH C F .E C lk .E[Q)EIEX|HI%EYE[jE[()*IE HGPh ; P 'P .=IE P_

7"U @ e; .=IE P_ ADC H'PQ? C EY C FTL C E)E C EADC H'PQ? C E L C E)E C E

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λ1 ¥V [ &([¥*7)EH\[ C E C * .DN E[X?E C E R+H C *'Pa)*

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Pa C \ . C Fh?d-( [ C HIE'55H'E(Pa)*Ë H]E"E[ )*'XX )*K=dkλ1M C F 5)*Pa

7*E)EHIgPh C N C Ik H'E(Pa)*g)E C F(Pa N K=[ &([λ0M GE[ X)*(5 DN_EQ*')-G .-Z j[ &([

C F5)*Pag?H(Pa"Pa()* * P_ ) ; * 5)*P* )*"*F *X|)**Fv gU @ U *[dkE[gX?)=()*Ph C H K=Pa<-G C & -Z)E&(g?X)* E M ? C H'PQ? C E C F_ C E)E C E VY.E[('&([_ C E)E C E%[5d-( [ &([)%X)*(5 DN!E"*')-G .-ZgE[5 C E[ C H'PQ? C E E[ )!X?)=()*Ph C Ha ! C d-()E&(hdkj)"E[5 C E[hX|)=()*Ph C Hh7+\[a C H'P | C E! C¬=(')gH* ? C FE[ )g\ C F5)*FFI-G R7E C gPQ'H[[ &([) $5()gH* A E["P_ C C F C F5)*F FI-G R7E C jE[aX|)=()*Ph C H_ "* Pa )Y=() E[_ C H'PQ? C E] C FuE[ C E)E C E aij C H) C C &X?)=()*Ph C H|E[uDNGX?" 5)*Pa F F~?! C H* A*A*A ¬k[)*λ0 C F

λ1 g[ &([v g[ *_FwH'Pa C EF C $ &(')*U K^G

*'P3'X 7E[)*j)*¨F;-7 C \&( C F!F EF;- C \&(l=()?E[! C \)N *H[Pa L C E)* C &)*.N *H')*+[ &([)X)* Ej7E[H(j"dk+) .=+ ;X?HI\ C HINZ ¨L C E)* C &]7j"R7E)X?( C !E Pa©FE¥Pa(*H')* .=©';X)*(Pa *W=Ikj)X)* E g[)*I=()*

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U @ U`)=()*Ph C H" ADC H'PQ? C EY C FTL C E)E C EADC H'PQ? C E L C E)E C E

i+7E Pa C EF Pa C \Fi+7E A c KeZJe c KJ(J( c KJ( n(nc U @ Ji+7E A*A @ UwJ n c K^ c ^ @ eZ c(n @ KJ @ Uw^i+7E A*A*A JG U @dc(cc K^(^(J @ @ ((U @ K^ @ Ui+7E A @ KeZ^(^ c KJ n c @ K c;@dcc KJ( n

E[] C E)NFH * C FX| C F C [dk C &aE[] C E)*X)* C ') C E C FEh)*Ph C C E[ '* C * hg[_PaX )* H C F C &(" Q1FIH gFIR K @dn(n M C F H7EQE[57! C )*.N© C E)Ndk+)*+\[" C .E ¬X)*(5 . .DNh ')*Y=()+E[5)*Pa %g[ |H'*"\["X C )* C &5)*Pa)*©'*'5.N©E )*H\[[ &([)-()E&(~)*I-Z C ' X5)E H'R)*.N¥ C E[ 5)*Ph)*(_X[5* ADC &( C )Eg . . (*)-(F¥E[57 E[[5)*F )E7EFH)**h_ 5)*P?H(Pah(F) jH'*©E[TH(PaX?IE .E .-(X)***')*©&( C )E7EF C E[T* P 'R<E CPaGF ?E[ )*.NT C E)E C E H CC "| C "=()Ph C NTX?)* GF .E[IN~)*Q' C *'HH**=' C PaX)*d-G C &E[ )EH\[ C ((&N( %dkjI-() G .%k ;?*[dk C ?dk¥E[57E[5 C w)*'X;EHIN)E7EaFH)** d-()!E[aH(')**WjE Pa =()] 5)*Pa] C F E[57Q7]] C E[a*[())*' C )*.N© C E)E C E"H C ;X?I)E . C HaR)*&()Y)E7E"¨X)* \ DN\[5 C C R7E)X[5*E["Ph)*(X)*wH*

03:x|sZ4h >?4dx76=sG

VYj*[dk C 7?d-ZwE[E Pa C E)Nh";¬HIE¨E[ ;X?HIEF .=IE P_ C FaE[YX)* \ DN 5)*P dkE[ C E)NFH * C (*)-(F3 C E[ * PQ'R7E . C )*R<\IF E E[*)*H[¥ C E C * .E I_ C F E[ C 'PQ|)_HI C *'Pa)*a Pa C F¥|<k" A _E') C a(';E[57]E[W C H C E .-(hET C E)]E[hPh)*(IQ C E[W C &T)*' C FX? C F C &Z7E .-(.N C E[*)*H[ C E C * . NWE[!HIE'5H'E(Pa)*|H'*Q C Ik 5)*PH CC ;X?HI_*H')*H'E(Pa)5* ADC $ &(')*+U @ (E[*( F . C +)*X)** C EE[ C 'PQ?)? C E)* g[ C 'P |)¬HIE'5H'E(Pa)* X?) 5)*P *[dk C ZN©E[ F*EF~ C ADC E[ I9H('P C ¬E[Q=(')H*H C H) C C &© Pa \7E -(a C E)* Q)*a .'E)E7EF C F C E[h)* &([Z!H('P C lE[hF Z;¬)* C *)*H[TH(YH C ER7E C +=() CC d-7E .-(" C E)* )*!&( .-( C gE E[57Y C $ &(')* U @

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20

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1=0.2

0 50 1000

20

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1=0.2

0 50 1000

20

40

60


1=0.4

0 50 1000

20

40

60


1=0.4

0 50 1000

20

40

60


1=0.6

0 50 1000

20

40

60


1=0.6

0 50 1000

20

40

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1=0.2

0 50 1000

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1=0.2

C 'PQ?) C E)* T¨HIE'5vH'E(Pa)*X|) 5)*P$ &(')* U @ GL C E)NYH * C C FVHIE'5i¨'*E(P_)*

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λ1+ a[ &([v g[©FH)**© C E)* h C E[TRhX[5*TE[TH* A*A

C F A*A*A +*QE)* C &(.Nh)*R7EFhE]\[FH)** C E[ C 'PQ?)+HIE'5¬H'E(Pa)* XADC H* A C F A %k[)*

λ1 adk Ë[ C 'PQ?)a Pa .\<E -Z C E)* a*PaaE ?

)*R7E .-(.NW\=()gE[ k[( E Pa K=)*&Z)*F C & E[ E)* C F M ADC E["H*! CC d-7E .-( C E)* QE[X57*E) C Q* Pa ) ADC E[R X[5*H* AA C F A*AA C X5)E H'R) C E)* *PEa?"X?(* .E .-(.NW)*R7EFE E[ C 'PQ?)HIE'5H'\Pa)* jVY=()+E[w'5 C E .\7E .-(g C .NG* ( Pa \7E -(g C F CC <-77E .-Z+ C E)* )*g C .NG*F E(&(IE[)%?H'*E["H()*)*R7E C +?IDk+ C E[P C FE[ C 'PQ?)HIE'5vH'E(Pa)*)*"* Pa ) !U @ ^ *[<kE[]HI()*)EIR7E C |I kj C E[ C 'PQ?I)Y C E)* Y C FE[ C 'PQ?)HIE'5¬H'E(Pa)*+ C E[ 5)*gH('P C ADC E[*H C FH('P C E[ C 'PQ?)jl Pa .\<E -Z C F CC d-7E .-( C E)* GHH')*)* C &_ C -Z)E&(" g)*X|()EFv

"U @ ^Gïj()*)*R7E C ?IDkj C VgHIE'5ij'E(Pa)*X?)$ )*P C FTL C E)* \ aH()*)*R7E C C E)*

i+*i+* A c c(n @ ^7Ui+* A*A c Kê n ^ @i+* A*A*A c K^((7U U ni+* A c c ê c ^7U

a"sbVa e Vf-$tau|q d eL`!bVa "u|q` k#_p Vfle[cu!a `!bVak#_u!u!apmc`!d _e k#_a jk#d ae `|qlvx_ul`!bVa)k#_u!u!a%qwrt_e"nod e.kcqwa%q~ "sbVa1eVf2$ au|qsd e `!bVaqwa%k#_e"nky_pmofle cu!a`!bVac#$au|c&aIae`!u!d a%qsvY_u/`!bVa /bo_pma1u!Ve~

A ?E[*)*H\[T C E C * .E )*"dk K=H* AM 5E[)*" C .N * &([wgH()*)*R7E C ?IDk+ CE[ C 'PQ?)a C E)* h C F¥E[ C 'PQ|)h7"HIE'5H'E(Pa)* g[T C H)**TYE[H()*)*R7E C Hw<aH C W=)*(PbH* A E H* A*AA hPh C N H'*FZN¥E[T C H)** C &y]1"sbVaSnoa%k#u!a%cqwaId e noafhce"nb"cq/cp u!a%cnoi$taaegd p p "q`!u|c`!a%n d e d Vu!aX"~ #o~

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"U @ ;ïj()*)*R7E C ?IDk+ C ij'E(Pa)*X?)$ )*P C FTL C E)* ¨¨N`%[5* a`%[5*

b`%[5* A `%[5* A*A `%[5* A*A*A

i+* H()*) C E)E . H()*) C E)* H()*) C E)* i+* A c KJ n U @ G U n c @ c;@ @ ; Z c @dc J @ G ni+* A*A c K^(Z^ @ G UwJ c KJ((J @ G ( c K(J @ J @ ; c i+* A*AA c e((eU @ ; U n c KJ7U @ @ G K^( c (Z^ n @ JG Kei+* A c @ ( @ @ ; e n c c eU(e @ ; @ c @ UwJ @ ; Z

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bb"cqwa%q #B'# #B'"ce"n ## #sk#_ $aus`!bVartau!d _VnVq

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λ0 C F

λ1 F Z<aH'.Y.E[('&([ .*PaE[57

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λ1 Tg[ C 'PQ?)]g C E)* ]

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g[W*(';E C 'PQ?)!g C E)* !F Z;¬)*!* &([wE N~ C %H*]+E[ 5)*]DkjTPh)*(IX[5* ADC X[5* A <Pa*l C E)* wHH') C E[¨H* A*A*A C F A dk[)*

λ0 l[ &([v `%[5*

A*A H[57)\7HIE)* F wNTE[_dk+ C 'P |) j C E)* ][)*!X[5* A RHw"H)E)*'HIE')*GX[5* A*A *[dkjE C F C HIN_Edk+)*F¨ C &Z<\ -Zg PaX5HI%

λ0 C E[-()E&(

C 'PQ?I) C E)* ADC X[5* A*A*A ;E["F Z;¬)* C H?H(Pa H)*) ¨$)*(P H* A E_H*A*A*A E[ C 'PQ?)g C E)* gFH)**YEF .N( ADC H* A 3E[)*])* Ph C NW C E)E C E 5*E[57j C E[YR¨X[5*YE[<k*)*H\[ C E C * .DN_vE[HIE'5|H'E(Pa)*+*IPajE]XRNE[hIN )*(_ C C F'H C & C E)* Tij C H) C C &TE[a C E)N C Ik 5)*Pa E[*h)**'.EH()*)*(?()E7E E[ C F C &(?d-("E[57E[ E Pa C & C E)NXdNG C PaX|()\ C g)*(=()E["FI-((XPa C 5)*Pa

@ UwJ


03:x|sZ4h l694<

$ &(')*U @ ! .'E)E7EE[Y5 C w)*'X;EHINh)E7E¨=()E[YF Z;¬)* C +H C ER7E C *)*H\[ C E C * .E I ] U @ W*'PaPh)* E[ 5 C w)*'X;EHINu)E7E=()E[ F Z;¬)* C "H*!F -G FFu C EWE[)* X[5* V9E)" 5)*"X[5*_jF'EPa C vE[)*_ W*X5 C E Pa7?(';e c X?)* wF |k[)*!E[!I-(l% ; .E C &5)*Pa H C * F)E.N[ &([H(PaX5)*FER7E)X|)* GF ADC H* A C F A ¬k[)*

λ1 .<k ¬E[ )E7E ¨ ; ." E[ dkj

ADC H* A*A C F A*A*A ?E[Q5 C w)*'X;EHIN©)E7EQ Y[ &([)=()h[ &([©*)*H\[u C E C * . N¨HE'5lH'E(Pa)*

λ1 +g[!*)*H\[© C E C * .DN7\["X?E C E RH C *'Pa)*

λ0|[5 C .N

* &([Z\ NhX?(* .E .-( PaX5HIg C \[ *\ C F57)EFFI-G R7E C VYgF *H'**Fk .E[)**X?HIEQE[ .=IE P_Y\[ 5)*Pag?d-Z5$ &(')*YU @ Q*[dkgE[57E[5 C w)*'X;EHIN )E7EgPh C .N!FX? C F¨ C E[*)*H\[a C E C * . N]?E[HIE'5H'E(Pa)* λ1 hg[h-Z)E&(_5 C w)*'X;EHIN )E7Ea ")*R7E .-(.N©dk=()"dk-7'!

λ1 * C E[

H* A C F A Q 5VYλ1 C H)** 5E["5 C w)*'X;EHIN)E7E C H)** | * ;E["()*F)E[

d-()E&(Q5 C w)*'X;EHIN~)E7EQ H* AA*A K c c e n M H* A*A K c c J(7U M H* A K c c;@ ( M g[]-Z)E&("5 C w)*'X;EHIN)E7E"H* A Pa(' C E+E c c J7UZ; VgFF .E C N

λ1*Pa

E C O ' C H C &Z7E .-Z.N"E[g*X5 C |E Paj' C E GE[g5 C w)*'X;EHIN )E7E+?H(Pa%)*R7E .-(.N\ g[QX HIE')*]|H(PaPa()*!F Z;¬)* C E R7EFk[ C E[!E[)*]X[5*")*] C .NG*F©*X5<)E7E.N %&( .-( C C .gU @ G $5();H*%E[5 C w)*'X;EHIN )E7EgFH)**¨=)*(PX[5*A E X[5* AA*A Zg[FH)**=)*(PX[5* A E"X[5* AA %R)*&()E[5 C E[FH)**=)*(P

"U @ G%+ C w)*'X;EHIN <\`%[5*

a`%[5* A `%[5* AA `%[5* A*A*A

i+*i+* A c c J7UZ c c;@ ^(^ c c;@ e @i+* A*A c c eZ(J c c J7U @ c c J @(@i+* A*A*A c c @ ^ c c eZJe c c JZJi+* A c c J n;@ c c J7UwJ c c J @(@

ab"cqwa%q #B'# #B'ce"n ###k#_ $au`!bVa/rtau!d _onVq

t = 1`!_ *.'

t = 34`!_ Y*Y.'oce"nt = 67

`!_ >*>V~

X[5* A*A E X[5* A*A*A C ?H* ¨g[ +Pa C jE[57+E[ Ph C F'EPa C +\(gXRH

@ UZe


0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

λ0=0.8, λ

1=0.2

Pa C · · · EF$ &(')*U @ ;+ C w)*'X;EHIN 7E

@ U(U


F')* C &hE[5)*Y kjPh7)EIX[5* ADC E[]E[ )*FTPh)*(IX[5*v ; .EYGHH') C .NT7a<k3)E7E ADC X[5* ¬E[]5 C w)*'X;EHINT)E7E! E[]<kjYkg[)*

λ1 dk ¬ C F©

C H)**jλ0 C F

λ1 C H)** ïj(PaX5)* C & H* A*A*A k .E[aH* A *[dkË[57%\[dk

λ1 C H* A XYE[]5 C w)*'X;EHINT)\<\!dk+)E[5 C C H* A*AA ¬VYE[]5 C w)*'X;EHIN

)E7E"H* A C H\[X[5*! g[ &([)+E[5 C C H* A 5 .gH C ?"H C H'FF 5E[57gE[5 C w)*'X;EHIN)E7E"*_ C H)** C

λ0 +[ C &Z7E .-( PaX5HIg

λ0 C E["5 C w)*'X;EHIN

)E7E C E[ X[5* AA C F A*A*A jE)* C &()+E[5 C C X[5* A g[ + +X)*(5.NhH'*FZNE["E)* C &aF'EPa C X)*wH*E["5 C w)*'X;EHIN)E7E F')* C &QE[ 5)* @dc X|)* GFg CH\[TH*

]2?>y(sG>?4dx<:;4<6=2?>:5>¦ t¬4d:)(6¡694\£ADC E[ *HIE C E[_ PaX5H"7Ë[_H C *'Pa)* l*)*H\[ ?[5-G (')" C E[_H(PaX|IE .E .-ZE)*'HIE')*hjE[a C F'E)Nu !E'F Fv WVPa*')*_=()"H C H C E)E7E C k[ .H[ k F.N'*F E[WI) C F57[¨ C F ¬ )*%\ .DN© C F !XX F C FF .E C EE[) C F5[ C F TEWHX;E')* *aE[QF;N C Pa HY C Ph)*I*[5)* g[ Y C H*E)N?H'* .% % PaX|(** Ë"H C H'FgPa)*.N]=)*(P [ &([ H C H C E)E7E C C F Qk[IE[)E[)*" gH(PaX?IE .E C K= *& 5( .&((X?(. .E .HX)* H"H(PaX|IE .E CM () C :K= E& 5_H7)*E M g[Q ; E C H %H C H C E)E7E C C F HY E[Q)**'.YE'F;NG C &W[dk Eh*'PaPh)* E[F E)* ';E C 7lPh)*I+*[5)*gPa C &5)*Paj C !* C &( C F aEQ?Y'*F C H C 7PaIE)* H! C F© C \ \)*'Y C .NG* @Bg[]Pa(YX|(X'R)Pa*')*!E[57Y .Pa C E C F 5=() C \ C H¨ C ACHzJ1RT? K @dn ( M QE[) C F5[g C F ¬ g[) C F5[g C F QF C F©*'PE["*w'5)*FTPh)*I*[5)*+5)*Pa A _\7E H Pa*')* E[57*[('F©?]PaXdNZFT C )*R7E C *[ XEhE[]X)* \ N 5)*Pa YVYYX?( C EF©(';ZNEGF F F P J K J c(c(cNM C FI-( C =')E[)PaX[5* FwN = FN@1AC? ] C F ?HzJ 1AlK @dn(n M .h a P_X?()\ C _E[57hH\[5 C &(W C Ph)*Ih*[5)*W|© C .NG*F +k[ H\[ aX5)E H'R)* NE)*'_=() E[aF C & 5)*Pa Wg[ K= C M 7 DN©+Ph)*I]*[5)*!H C ?_-G IkjF ]Pa*')*=()H(PaX?IE .E .-( C * wk[)*+ .¨ ¨ PaX|(** +E]&Z C Ph C N_ C * &([ZE¨ C E"E[' C F)*.NG C &WH(PaX?IE .E .-("=()*HwN© C .NG* C &WhH C H C E)E7E C C F © C .N L Pa C C &PaX )* H5F57\!=()j*I-()Ev C F'E)* ¨=()E[YN()* @dn n @dn ( = FN@1AC? C F ?HzJ 1AK @dn(n M =(' C F [ &([.N©-)NG C &TPh)*I]*[5)*]k \[ C E[h&()*('X +E[aE(XG -( 5)*Pa #aa2 57:J1 -@+;=>*?*?.'r~I* #Ay~ _u aflrVd u!dmkcpsq`!"nod a%q%' H9Ud8]SR -@+.2 /%+.+ ;=>*?*>.'Tr~ >*Y*Y@Aqw.*a%q`|qS`!_)"qwagk#_e"k#ae`!u|c`!d _e u|c`!d _ q7cq

cp `!au!e"c`!d $a$ a%kc"qwaI`!bVai cu!a/dmnoap ijrV&$Vp dmqwbVa%nN~

@ Uw^


ij(PaX5)*FE_E["E')*' C H! C Ph)*(I*[5)* |H C H C E)E7E C H\[5 C &(FT*dk.N( ¨g[INH C H'F!E[57H C H C E)E7E C C F©H(PaX|IE .E .-( C *)*"DkjWF E C HIH\[5)EHIE)* E H C C F'E)Nhk[ H\[)* [5)*F.Nh)*R7EFv $5')E[) ;E[ )+E Ph7E C j&( .-( )* *YE_| I-ZE[57 C FQ CC d-7E C ";¬HIE[jF;N C Pa H5Ph)*(I*[5)*%lk+GH C H C E)E<E C E ]&()*7+ GE C g[57][ &([h CC <-77E C C E C * .DNaPhNaH'* H C HI C E)E7E C EFH C g *[dk C w=()% C \ C HwZN>E J FWX F K @dn Z^ M C F XIH9? P K @n(n M VHIH()*F C & EE[|<-(DPa C E C F .EPaH C H) C C &"Ph)*I%E)*'HIE')E ZE[ *HIE C F .-G FF C E]E[)*"X5)E $ )* GE[ 5)*P D* F E)* ';E C +)* E'F Fv jOGH C F 5H C H C \)E7E C C F H C Pa.N"E[g) C F5[ C F C FQE[g()* C +H')-()*jHH'R7EF C FX)* \ DNh gPa*')*Fv g[ )*F.N 5 \ .DNh C F C .NG*Fv

@ ACH U#VA ?G=-A P H9A 9P ACJ1B VgHH()*F C &!E 9P/P J1B K @dn(n M 5)*P D* F E)* ';E C )*9E C E .Pa )E¨'`)*IE ()(& C ()*PhlF E)* ';E C A FPa C E)E7EF~E[57E[ F E)* ';E C (;\ C FwNWE[ * PQ'R7E . C k+¬E_E["(& C ()*Ph¬F E)* ';E C *'.Eg=()F Z;¬)* C *)*H\[T C E C * .E )* H(PaX5)*Fv g[jF E)* ';E C l 5)*P * j)*¨*[dk C C $ &(')*U @dn g[jX? E[jF C * .DNK=PaGF M Pad-(+EQE[ )* &([Z+=)*(PX[5* A E X[5* A*A =()+¬H* ADC X[5* A*A*A E[YPawFE') C j57H E"E[YI9=()¨5H* ADC E)*E C &(.N w=()%E[YH* A*A C FA*A*A (\[Pad-ZPa C ¨¬E[PawFgE"E[)* &([Z %=(dkjFaZN_ .%E') C C &!5H\ Pa()*F)EE H.N!E[5 C C E[H* A C F A Q Zg[w' wE[)E C FP;¬HI¨?E[X?E C E RH C *'Pa)* F(Pa C C % C E[gH* A C F A Q ADC E[gH* A*A C F A*A*A E[g*)*H\[HIE .-G .DNE[ HIE .-(QH C *'Pa)* XRNG WPa()*] PaX|()\ C Y)*( g[)*I=()*vE[-Z)E&(_HX .\%EGH\u C H)**]Pa()*_PawF)E7E.N~ .jH'E(Pa)*])*aPa()*_X)* H7*E C E .-Z g[!EPa" +- FW=()gE[!NGPaPaIE)N 5 * E["F E)* ';E C g|H(PaPa()*+ C FQPa()*j)* &([ZD*(IkjF C H* AA C F AA*A E Pa¨X5** Zk[I)E% C H*A C F A E[YF E)* ';E C ¨)*YPa(¨NGPaPaIE)* H C X[5* A*AA Gg[*Ik C E+EE[)* &[w%Pa C E[57% C E C * .-(.NQ*)*H\[ C &!HIE'5H'E(Pa)* C -((.-(g*(Pa 5)*PaET|h*'HH*='¨k .E[uE[ )!HX .\HH'PQ'R7E C K=|H'*hE[IN )*a)*Ik+)*FFZNuWR)*&(QH'E(Pa)5* k[ C H\[5)*&( C &dk X)* H M ]g[ FG C !7XX.NTEE[aPh)*IE A C F A k[)*_E[a)E C F(P ;¬HQF(Pa C 7E ag[aX?~jE[F C * .DN XX?)*!\T?h<kjQ C X[5* A*A g[ ]H C ?h ;XR C F ZN E[hHI

@ UZ


0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.4, λ

1=0.2; t=20

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.4, λ

1=0.2; t=60

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.4; λ

1=0.2; t=100

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.6, λ

1=0.4; t=20

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.6, λ

1=0.4; t=60

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.6, λ

1=0.4; t=100

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.8, λ

1=0.6; t=20

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.8, λ

1=0.6; t=60

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.8, λ

1=0.6; t=100

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.8, λ

1=0.2; t=20

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.8, λ

1=0.2; t=60

0 50 100 1500

0.01

0.02

0.03

0.04

0.05

λ0=0.8, λ

1=0.2; t=100

$ &(')*U @dn $ )*P D* Y \)* ';E C

@ Uw


E[57 C X[5* A*A \[gHX .\5HH'PQ'R7E C F .-()*&(?H'*vF Z;¬I)E C H¨ C E[F'EPa C 5)*Pa VY"FGH'Pa C EF C U @ K= C X5&( @ U nNM vE[_Pa C ?H(Pa![ &[) =)*(PX[5* A EaX[5* AA C FTFH)**=)*(P X[5* AA EhX[5* A*AA =()YH* VY*[dk C C $ &(')*U @dn GE[ + +F )*HIE.Nh)*R7EFh\QE[Pa<-(Pa C glE[ F E)* 'GE C ag[_Pa C ! C X[5* A H CC !?aH.)*.Nu)*)E C &(Fv h<kjI-() C X[5*A*A E[QPa C YH* A*A C F A*A*A K=U eZ^(Jh C F©U U @ J7U M )*][ &([)E[5 C E[(*QH* A C F A K=U @ c Uh C FTU e c J( M ADC X[5* A*A*A E[])*R7E C H\[5 C &(!*hE[57E[Pa C ¨vH* A C F A Ke; n U @ U] C FhU @ J(e M )*[ &([)%E[5 C E[(*vH*A*A C F A*A*A Ke; nG@ J n C Fhe; n (e M g[ ¨*'&(&(E¨E[57¨ C E[ C F w\[d-()E&(HXG .\vHH'PQ'R7E C FX| C FPa()*E)* C &(.NW C E["*)*H\[ C E C * .DNWlE["HIE'5H'E(Pa)*

λ1;E[5 C C E["*)*H[ C E C * . NWE["X?E C E RvH C *'Pa)*

λ0

g[h\ C F5)*F FI-G R7E C =()"H* A*A*A C HI)E*QPa C E C H NT=)EP X[5* A EX[5* A*AA |$5()+H* A C F A E[ \ C F5)*FFI-G R7E C 5)* C H)** C FE[)*79E)FH)** Qg[_EPaQ Y-7 FT=()H* A*A vg[ FH)** =)*(P X[5* A*A EX[5* AA*A C 7gF E C HI+E[ FH)**"H* A C F A Q g[ gPa C +E[57 C TPh)*IQkg[)*WE[W*)*H\[ C E C * .DN HIE'5¨H'E(Pa)*

λ1 ][ &([ E[

HX .\HH'PQ'R7E C H C F .-ZI)E&"H C * F)E.N( _U @ *[dk!E[a)**'.E!¨\[ Y(Pa&(()*d-ZOGP_ .) C <-T&(GGF C * DR "E=()E[](& C ()*PhF E)* ';E C ADC ]U @dn |E[])EIE' \Y%E[ (Pa(&()*d-ZOGPa ) C d- &(GwF C * DR E=()E[j`)*IEYF E)* ';E C )*X)** C EFv g[ C '[ZNGX?E[* %(& C ()*PhvF E)* ';E C H CC ?])* HIEF©=()Pa(YE[]H*7jE[Y* & C 5H C HYI-(? n ^"X?)jH C L ;HX;E C g)*E[X[5* A C F A*A H* AA*A C E[YH C E)E)NGE[ C '?[ZNGX?E[* j`)*IEQF E)* ';E C H CC +?HHX;EFW7E[ n ^X?)H C jI-(=() C N H* %g[ % C *')*X)* * C &"?H'*Y H C * .N?"-Z)* 5FT C $ &(')*"U @dn E[57_&()*7YFlE[]X)*(5 DNPh7E C E[_I9"¨E[_PawF C F E)* ';E C jH'*aj(';E )* vE[ <kj)?(' C F

x0*[dk C !H)%NG\IPk .E[a)**X|HIjE

λ0()

λ1 g[E Ph7E?E[

X5)EPaIE)\ lE[ H\ C * av C H)**Q=)*(P X[5* A EX[5* A*A*A =()YPa(

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!H0

dmqsu!a%Ca%ky`!a%n d v`!bVa1`!a%q`9q`|c`!dmq`!dYk ;( .Aza10Vk#aa%nVqsd `|q/k#u!d `!dmkcp9$cp VaE;Zk $.Ay~

@ UZ

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ax0

2 R =H =S 6 S 8 9: ; 7 < 4 S O 5 7A 4 56 7? 4 2 T 4 = 5 O 4 C 4 S 7: 7C? 0 1 2 34 56 78 9: ; 7 : 7< : < : 4 : =< : =>@? > A 2 BC =: => 4 5A 4 56 7 4 : : ; 7 DE F < =GH = I> 4H > 7 5 7A 7 5?


t = 100?

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ax0

2 R =H =S 6 S 8 9: ; 7 < 4 S O 5 7A 4 56 7? 4 2 T 4 = 5 O 4 C 4 S 7: 7C? 0 1 2 34 56 78 9: ; 7 : 7< : < : 4 : =< : =>@? > A 2 BC =: => 4 5A 4 56 7 4 : : ; 7 DE F < =GH = I> 4H > 7 5 7A 7 5?


t = 100?@ Un


g[ )**'.EglE[ (Pa(&(()<-ZOGP_ .) C d-a&(GwF C * DR gE)*' C PQ &('(' $5()+E[ F57\ E["* PQ'R7E . C PaGF 15)*Pa+k ¬? F E)* ';EFHH()*F C & Ea(& C ()*PhF E)* ';E C vk[ H\[ H()*)**X? C F!EE[ C F C &("+Ph C N~PaX )* HE'F WL%PaX )* HI-G F C Hh[5!*| C =(' C F =()E[h`)*IEF E)* ';E C A Q*Pa]E©?Wg*H C F5)N PaX|()\ C H_k[ H[ DNGX?WF E)* ';E C Pa)*&( A YPa()*! PaX?()\ C E C F~(';E[]=()*HYE[57Y C F'H h*IkjFuF \)* ';E Cdk C &g=()(';E )* Yw-G ('*.N <E[j* P 'R<E C PaGFw HX5EY)*H C E)*'HIE[ gDNG FHI %V3X|(** PaX5HI+ C E[ NGX|"F E)* ';E C PhNW[5-( E[H C E)E C !wN~E[_)*w' )*F Pa C P]'P<aH C ]*H W$ )*Pa ?dkE[aH)* .E H* [5-(E" ; .%E[Ph)*I g[ %<kj)%?(' C Fa PaX. .E C F C HIN_Edk+)*F%E[(& C ()*Ph¬ C FTk+dNW=)*(PE[!`)*IEaF E)* ';E C ADC hU KJ c ]*[dk C [dkE[ 5)*P * W !)*R7EF EE[ C 'PQ?)]HIE'5H'E(Pa)*% C FQEYE[+X)* E=().GH* (k[)*+E[)*+X[5*)*jF E C &(' *[Fv $5()vH\[!X[5*<E[%I9H('P C H C 7 C vE[%H()*)*R7E C HG<aH C l?IDk+ C 5)*P* _ C FuHIE'5H'E(Pa)* ADC E[ *H C FuH('P C ¬E[ H()*)*R7E C HG<aH C E?IDkj C 5)*P* I! C FX)* E)* )*X?()EFv

WU KJ c Wi¨()*)EIR7E C jIDkj C $ )*P OG C F 'PQ?)QYij'E(Pa)* C FT$ )*POG ! C F`%)* E`%[5*

a`%[5* A `%[5* A*A `%[5* AA*A

i+* H'E(Pa)* X)* E H'E(PaI)E X)* E H'E(Pa)* X)* Ei+* A c K(eZ c ZJ @ c K n e c eZ n;@ c K^Z7U c e @ ^7Ui+* AA c K^(ZJ c @ J( c K c Z c K^ @ U c ZJ @ c Uw^î+* AA*A c K^(J @ c K^( c(n c Kê((e c U n(c c U @ U(U c K^ c Zi+* A c K @ ^7U c KeZ^7U c Z^ZJ c Kê(ZJ c K c J c U @n ^

ab"cqwa%q$#B'##B'"ce"n## #zcu!a1u!arVu!a%qwae`!a%n $ih`!bVaSr au!d _onVq

t = 20't = 60

'"ce"nt = 100

~

U KJ c )*I-(_~H)*.N X|(* .E .-ZWH()*)*R7E C ?IDk+ C E[d-()E&(* E[5)*Pah C F¥E[E\ C 'P |)a HIE .-ZH'E(Pa)* ADC E[Ph)*(IaX[5*A C F A*A %E[H()*)*R7E C ?IDkj C 5)*P#* T C F E[ C 'P |)aH'E(Pa)*a [ &([)+=()gdk -'

λ1K=H* A C F A M 5g[)*5E["H'E(Pa)*\N C &()

7QE[EPa 5)*P E[5 C C H* A*A C F A*A*A VY_~H C *w' C H+ 5)*P k .E[¥R)*&(aH'E(Pa)]5*h ]_E©&()*dk * C Hh .! Q*T*[dk C C E[a\_E[57

@ ^ c


C H* A C F A E[5)*P * _[ &([.N H()*)*R7EF k .E[¥X)* E_ C X[5* A ADC X[5* A*A E[H()*)*R7E C |I kj C E[ C 'PQ?) YH'E(Pa)*h C F E[ 5)*P* W ]I-( C [ &([)!=()!E[hH* A C F A k[)*WE[W*)*H\[ C E C * .DN gE[HIE'5H'E(Pa)*h _dk" g[TH()*)*R7E C ?IDk+ C 5)*Pb* I© C FX)* Ea[5FH)**F k[I)E_E[_FH)**h "R)*&()=() H* A C F A k .E[ dk

λ1 ADC

X[5* A*AA %E[H()*)*R7E C ?IDkj C H'E(Pa)*a C F 5)*P * FH)**a=()aH* k[)*E[W[ &([_H()*)*R7E C H C E ¨|W=(' C F C H* A Q % C .NFTE[ 5)*Pa][5-ZT)*R7E .-(.Nu\ C 'PQ?)]X57E)* C C &TH'E(Pa)* E[IN* [5-( C 'Pa)*(' C IkH'E(Pa)*hk[ )*T)E C F(Pa.N F E)* ';EFv 3L ;HX;=()YH* A*A*A vE[QH()*)*R7E C HG<aH C E?IDk+ C 5)*P * C F©X)* E[5-Z)*H\[FhE[ )dk+¨I-(| C X[5* A*AA G$ )*Pa%&()*<kE)¨ .?E[INaH C XhE[ )X57E)* C C &"H'E(Pa)*j* .N_ C Fh . wFF .E C . N (E[)*)*Ph C N H C *'Pa)*j CE["Ph)*Ik[(P E[INH C 7*E)EHIg=)*(PE[ )gH(PaX?IE .E()*

JG J1B ?B P H/F P ACJ1B B5XIA ? g[ swx >¦l:5r¡Y6>¦ls h\ C F5)*FuPa*')*QH C H C E)E7E C 5)*Pa C Ph)*I A gF C F©

Ht =∑

i∈Zt

s2it,

k[)*sit \[gPh)*(I*[5)*+5)*P

i7%E Pa

t ADC E[H*v Pa C (X?(.N E[

) C F5[¬ C F h ¨w'5?E] C [ C FF .E C )5)*Paj C E)jE[YPh)*I wE[ C F FH)** g[)*H X)*GH7¨-'WgE[) C F5[+ C F Pa*')*QE[C 'P |)! 5)*Pa"E[57Q)*a C E[aPh)*(I!' C F)!E[W**'PaX;E C E[57Q 5)*Pa)*YvE[YEPa* $ &(')*U KJ c 'E)E7E%E[YFI-((XPa C jE[I) C F57[ C F C E[ =(')gPh)*IE g[g) C F5[; C F Q C H)** C Z=(')H*%d-()E[jH(')**gE Pa L ;HX;=()WH* A*A*A jk[I)E~?7\[ &()*('XW"H C *'Pa)**)*H[ k .E[ [ &([ C E C * .DN E[aH C H C E)E7E C FH C " C X[5* A*A*A

λ1*Pa"E[5d-(_E[_Ph C C O ' C H

C E[T*[5X|©E[TH C H C E)E7E C C F ¬ Ow\)E C &u=)*(P XX)* ; Ph7E.N E[EPa©I-( C C H)**© C E[© C F H C ?©(*)-ZF C H*'XE H)\ C X|)* GFv A +H* A K c c ^ c ^ M H(PaX5)*FuEH* A K c c Z^7U M C X|)* GF

%[#aa1a~("~ 57:J1 -@+;=>*?*?.'rVr~I* #Ay~

@ ^ @


0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

λ0=0.8, λ

1=0.2

¨) C F5[l C F · · · EF$ &(')* U KJ c ) C F5[ ADC F

@ ^(J


t = 20|E[] C H)**] )*R7E .-(.NPaGF)E7E] C F-)* C .N* &[wE NF'!EaE[

F Z;¬)* C *)*H\[T C E C * .E gX?E C E RvH C *'Pa)* λ0 g[" C H)**"F'"E

λ1 YE)* C &() ¬E[Q[ &([)E[Q*)*H\[u C E C * . N¨HIE'5H'E(Pa)* λ1v H* A

K c c ^ c ^ M H* AA K c c(n UZ M H* AA*A K c @ ZJ M C X|)* GFt = 20

g[" C H)** C E[_) C F5[ C F ~ I-( C E)* C &() C X|)* GF

t = 60 !g[)*l . H* A

K c @ JU M H* A*A K c e c ^( M H* A*A*A K c e( c M C F H* A K c @ ^(^ M C E[F(Ph C %H* A ADC E[]RYX[5*]E[])*' C C Pa.N=)*(P |(';

t = 75 C

E[aH C H C E)E7E C C F *<kg!Fdk C C =(')"H* WVg"E[a C F jE[a)*' CKt = 100

M 5E[!F Z;¬)* C Ph)*IE C F©'Xk \[T C C F E[57Pa(' C EgEaH* AK c @ eZJ(^ M H* A*A K c KJ7UZZ^ M H* A*A*A K c e( n;@VM v C FuH7E A K c @(@ eU M * Pa )EH* A ij* A K

λ0 = 0.4λ1 = 0.2

M C F A Kλ0 = 0.8

λ1 = 0.2

M F Z;¬) CE[FI-Z(XPa C glE[H C H C E)E7E C Pa*')* ADC H* A E[ C F C H)**E) C F E[_-'])*h?d-(aE[(*agH* A 'X EE[hPa ; P 'P a[ CE[h C F C H* A E[hFH C h "E)!E[5 C C H* A *TE[57] C E[ C FE[")*' C 5H* A H* A C -()E&(E[" C F H* A K c @(@ ^ nNM R)*&()lE[5 C C H* A K c @dc J M VHH()*F C &YEYE[+ C O ' C H+

λ1E[j()*F)5E[

Ph)*IEY +H* A K c @dc J( M H* A*A K c KJ @ nNM H* A*A*A K c KJUU M gg[)*I=()* C H C H C H'FE[57jHH()*F C & E"E[Y) C F5[| C F ;"Ph7)EI¨ %E[Pa()*H C H C E)E7EFE["[ &([)+E["*)*H\[T C E C * .DNE[!HIE'5vH'E(Pa)*

λ15

g[ 2|x<sG>3yZ¢lxd8?s C E[)WX?(** N¥! .'E)E7E C & E[~H C H C E)E7E C $5()+E[ H C H C E)E7E C 5)*P * ! C FX)* E E[!()* C "H')-(Y)*"*[dk C C$ &(')*U KJ @ C FU KJ(JG j$5)gE["X)** C \7E C E[]()* C !H')-(] DNGX H)*' C "H\[(* C hg[a*( Fu C )*X)** C E!E[aH C H C E)E7E C =()E[aX|)* GF

t = 20

g[!F5*[F C \ C F=()t = 60

5 C FE["F*EF C Y=()t = 100

g[¨H C H C E)E7E C ;HX .\Z*[dk C C $ &(')*%U KJ @ H C |jXX)* ; Ph7E.NY)E C (F!X[5* A*A X[5* A X[5* A*A*A =()!%H* C .N©=()!H* A*A*A k[)*

λ1 ])*R7E .-(.Nu[ &([ E[hH C H C E)E7E C HX .\ C X[5* A*AA QXX)* ; Ph7E.Nw'5(EgE[%H C H C E)E7E C C X[5* A g[ )**'.l PaX )* H. NXR'* ADC E[)*.NX[5*]E[]Ph)*IYFI-((XPa C |E[QHH'PQ'R7E C %HX .\lF .-()*&( k[)*Y C R7E)gPh)*IX[5*E[]HH'PQ'R7E C HX .\¬E C FEaH C -()*&( C E["H)*(* D*HIE C F57\; g[()* C H')-(j=()%E[X)* E+)**[<k C C $ &(')*U KJ(JG g[H C H C E)E7E C X)* EhH C ?T)E C (F hX[5* AA*A X[5* A X[5* A*A C .N =()hH*

@ ^e


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.4, λ

1=0.2

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.6, λ

1=0.4

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.8, λ

1=0.6

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.8, λ

1=0.2

X[5* A ;%X[5* A*A · · · X[5* A*A*A$ .&(')* U KJ @ ()* C ]ij')-("=()i+X .\

A*A*A k[)*λ1 h)*R7E .-(.N [ &([ jE[TH C H C E)\<\ . C "X)* Eh C X[5* A*A*A

XX)* ; Ph7E.N~E[EPaWQ C X[57E A g[ QPa C ]E[57 C TPh)*(I]k .E[ PaGF)E7E*)*H\[ C E C * .DN_7HIE'5?H'E(Pa)*

λ1GE[H C H C E)E7E C X)* E

[ &([v [ C \[YHIE'5|H'E(Pa)*¨[5-ZY![ &([a*)*H\[W C E C * .DNa¨ C H* A*A*A E["H C H C E)E7E C X)* E)*Ph C +dk" ADC E)*E C &(.N C $ &(')*%U KJ @ C FQ$ &(')*U KJ(J <E[¨H C H C E)E7E C X)E\Pad-((XX?(* .EE[H C H C E)E7E C 5)*P * g[)*I=()*7E[% C -()**)*R7E C C F H7EE[57 . +kj()E[wk[ C .NG* C & E["Ph)*IE)*'HIE')*! C Pa()* FI\

@ ^7U


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.4, λ

1=0.2

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.6, λ

1=0.4

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.8, λ

1=0.6

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ0=0.8, λ

1=0.2

X[5* A ;%X[5* A*A · · · X[5* A*A*A$ &(')*U KJ(JG()* C ]ij')-("=()`%)* E

FIRT?BV?? K @dn n vXv n ( M )*X?()E!!DNG FuHI"E[57 C H)*(* D*HIE CH(PaX5)* * C _ C -((.-G C &uPh)*IEa C E[EPa C F'E)N +*) H C H C E)E7E C X?(* .E .-(.N])*R7EF E E[I-(5¬X)* HI A ?E[-()E&(X)* H w)*X|()EFa C U @dc ;)*H(P_X5)*FWE]E[YH C H C E)E7E C C F GE[ C F C &(+ FIRT?BV??K @dn nNM |E[57YE[QI-(E[QX)* H!=(dkE[QEPa]X57*E) C YE[ I) C F57[ C F Q|Ph)*IH C H C E)E7E C H C ?+H C 5)*PaF]=()E[ 5)*Dkj Ph)*IX[5* C E[ C ()*Ph H* A A*A | C F AA*A ADC X[5* AA*A 5E[")*R7E C *[ X?IDkj C E[

@ ^(^


X)* HQI-( C F~H C H C E)E7E C )*H X)*wH g[_-()E&( X)* H] [ &([)Y .%E[H C H C E)E7E C gdk" *'\ C E R7EË[g C .NG* 75E[+H C H C E)E7E C ( C FF .E C EYE[gI) C F57[ C F E[ x<2 4d:)(6¡6R4£ 5)*Pa" E'F Fv ADC E[_*[()!)*' C \[_X)* HDH*Ph)*&( C '*FuE C .NG*]E[ Ph)*I X?dkj) j 5)*P "g[_[ &([I)YE[ X)* HH(gPh)*&( C ZE[Pa()* .jE[X)* H?d-ZPh)*&( C 5H(E 5 E GE[[ &([)j Ë[Pa C (X?(.N~X|dk+)]g5)*P ADC E[h C &)*' C C ] C .NuFE[hX)* E![5d-(aEHd-Z)+-)* RYH(E E[IN* [5-( E Hd-()gE[ ;FH(E g[*!)* Ph C NH(E!H C H) C C &E[aHX .\EGH\ * C E)*Q C F FX)*H R7E C ag[)*I=()*E[aX)* H_Ph)*w'X *I] C )*R7E C EE[_ C &7D)*' C -Z)E&(_H(E WVgHH()*F C &E FIRT?BV?? K @dn n 5XXv n cNM C _H(PaX?IE .E .-( Ph)*I .PQ'[(FE[57E["X)* H w'5d-()E&("H(E 5 E

Pit − cit − (ρ+ δ) · Kit

Qit

Pit= 0,

K=U @VM

k[)*Pit

Y\[ X)* HQ 5)*Pi C C X?)* GF

tcit)*QE[Q-)* R]X)*GF'HIE C

H(E Kit

]E[WHX .\jEGH\ Qit

]E[(';EX'; X)*GF'HF ρ ]E[ C E)*

)E7E| C Fδ +E[")E7E FX)*H R7E C

g[!X)* H\DH(Ph)*&( C K `ï S M gF C F©

PCM :=Pit ·Qit − cit ·Qit

Pit ·Qit

,

* dE[F Z;¬)* C HG)*I-Z C ' C F -)* RH(l C X)*(X?()E C EgE[)*I-( C ' C F) H(PaX|IE .E .-ZaH C F .E C !E[`ï S *[('F w'5Ë[)*w' )*F )* C \+ C**IE%PaXdNZFQX|)Pa C I\)N]' C .?E.jK V M C -()E&( * C & L%w'57E CK=U @VM ;E[ V3 gF C F©

RRA := (ρ+ δ) · Kit

Pit ·Qit

.

ADC \[ C & )*' C jE[©`ï S C FG C hH C \ C E[T)*I-7 C h C =()*Ph<E C?H'*¨gX)* H%?d-(Ph)*&( C 7H(ElFG C l PaX NX?(* .E .-(X)* E %ij(PaX5)*FEE[ V 5)*P[5 E[_Pa()* Pa C (X?(.NTX?dk+) lE[_ &(&()E[_F Z;¬)* C H

@ ^


U KJ @ `%)* \ Nh$ )*Pa a`%[5*

b`%[5* A `%[5* A*A `%[5* AA*A

i+* $ )*Pac

`ï S V `ï S V `ï S Vi+* A OGPh e; U @ JG U c e( JG c n U

S F 'P e; @(@(@dn @ Uw^((J @ @ eZ^ nl)*&( c ( @ c KJ^Z^ c KJ @ ^(J

i+* A*A OGPh U n(c ^7U U K^(eZJ e; n(c J @S F 'P e; e((Z @ UZe c @ Z c Jl)*&( c c ( c c K^7Z^ n c KêU(U

i+* A*A*A OGPh ^G KZJ ^G KZJ7U ^G UweZJS F 'P e; c;@ ^ c @ eZ^Z^ @ (eZ^(Jl)*&( c @ @ J c n;@dc c Uw7U

i+* A OGPh ; Uw^( U c (eU e; KJ c UwS F 'P ^G eZ^(^ n JG e n ^ n @ e(( @l)*&( @ KJ n;@ c c;@ J( c @(@dc J

a 1j u!dmk#a Ck#_ q`sfhcud e ^ /aa` Vd u!a%n u!ae `|cpN_egcq!qwa#`|q~

bb"cqwa%q #B' # #B'tce"n"###/k#_ $a#u/`!bVa7rtau!d _onVq

t = 1`!_ *.'

t = 34`!_ Y*Y.'tce"n

t = 67`!_ >*>V~c _uhqwd flrVp dmk#d ì*'`!_ nodmq`!d e.Vdmqwb $ a#` zaae qwfhcp p 'fla%nod Vfce"n pmcua "u!fhq%' `!bVa`!_`|cpNeVf-$tau9_v "u!fhqsb"cq $ aaeaa` "cp p i nod $dmnoa%nd e `!_ `!bVu!aaSr"cuw`|q~

?IDkj C E[u`ï S C FE[ V 3g[~)**'.E)*©*'PaPh)* F C U KJ @ C

A a C E HhE[57 =()_+H*_ C +X[5*_*Ph 5)*Pa [5-(E[[ &([I*X)* \ DN %Pa*')*F¥ZN E[F Z;¬)* C H|I kj C `ï S C F V] S F 'P * F 5)*Pa)*u*X)* \©E[5 C *Ph 5)*Pa g[ukj()*TX)* \ DN (;\ C FhwN_E[YR)*&(5)*Pa wk[ H\[W C *(PaH*+I-Z C H CC +Hd-()jE[ )¨ C &7)*' C -()E&(_H(E * ¬E[ ) X)* \ NT C &(7E .-Z g[_F Z;¬)* C H_?IDk+ CE[]`ï S C FE[ V FH)**=)*(PX[5* A EaX[5* A*A*A =()gE[!*Phv C FPaF 'P D* F 5)*Pa C Pa( H* ADC H* E[ )E7E Ë[ FH)** g[ &([)j=()+E["PaF 'PQD* F5)*Pa+E[5 C =()g*Ph+5)*Pa $5()jE["R7)E& 5)*Pa

f "sbVaSqwd e.p a$cp Va%qvx_us`!bVa 1j\ce"nj`!bVa ^ cu!a1u!art_uw`!a%njd e " c$Vp a 7~ ' ^9rVrtae"nod 0 'Vr~F>@o~

@ ^(


X)* \ DN FH)**+=)*(PX[5* A E]X[5* A*A ADC X[5* A*A*A .¨'*'5.N_ ;HFE["I-(X[5* AA

ij C H) C C &QE[Y C O ' C HE[*)*H\[HIE .-G .E .Ë[H C *'Pa)* ;E[YX HIE')* "Pa ;Fv ADC X[5* A E[aX)* \ DN©jE[_*Ph PaF 'P D* F C F R)*&(5)*Pa!FX? C FQX?(* .E .-(.N~ C E[h*)*H\[ HIE .-G .E "jE[hX?E C E R%H C *'Pa)* λ0 g[uPaF 'P D* F 5)*Pa)*u* * &([ZE.N C &Z7E .-(.N C O ' C HF ZNE[

*)*H\[HIE .-G .E ]E[HIE'5+H'E(Pa)* λ1 g[ C &Z7E .-( PaX5HIQ

λ1

I-( C E)* C &()h=()hR)*&(5)*Pa ADC X[5* A*A λ0*E .[5W X|(* .E .-Z;¬HI C

E[WX)* \ DNu 5)*Pa ©g[ C &Z7E .-(h PaX5HI]λ1 C E[WX)* \ DN

PaIF 'P D* F 5)*Pa_[5hE)* C &E[ C Fv C E[H C E)E)N jE[TX)* \ DNjE[_*Ph 5)*Pa"*Pa"E?_X?(* .E .-(.N© C O ' C HF ZN

λ1 ADC X[5* A*AA E[

F(Pa C 7E C & ;¬HI=()aE[~*Ph 5)*PaW?H(Paλ1 S F 'P D* F 5)*PaW)*

FF .E C jE E[X?(* .E .-( PaX5HIaλ0* &([wE N X|(* .E .-(.N C O ' C HFwN

λ1

C .Nh=()+E["R)*&( 5)*Pa C E[ C &_[57H[5 C &(Fd-Z)gE[ k[(E Pa

g[!*Ph 5)*Pa*P Ea[5-("E[!Pa(YF;-7 C \&(<-()E["E[)5)*Pa .E[*)*H\[ C E C * . N~jE[aX?E C E R%H C *'Pa)*

λ0 "[ &([ l E C H* A*AA C F

A Q Y'QEWE[ .)*Phl*Hv*Ph 5)EP_H C *E[]k[( Pa(' C YE[57k+X)*GF'HFhE])E C F(Pa.N Ph7EH\[FWH C *'Pa)* $5()%E[YR)*&( 5)*Pa¨ .j ¨ .PaX?()\ C E[57 H'E(Pa)* ? X; ]+[)*I=()*E[ R)*&(5)*Pa(;\ C E[ |!)**'.E CH* A C F A lk[)*

λ1 !dk" l)*&( 5)*Pa>K=[5-(aE M t;¬)!<kj)!X)* H] C

-Z)E&(

g[]*(';E -'E[]`ï S C FE[ V )*!FwH'Pa C EFT C ] KJ VYXX? C F ;Xv @dn JG A +*[dkjE[57jE[*(';E-'YvE[YX)* HDH(DPh)*&( C C Pa(jH* C FX[5*+ Ë[R)*&(j=()¨*Ph!5)*Pag C FhE[dkj+=()jR)*&(5)*Pa Tg[hPaF 'P D* F 5)*Pa!'*'5.N H[ I-(WTX)* HDH(QPh)*&( C E[57] ?IDkj C E[`ï S |E[+*Ph; C F R)*&( 5)EP_ g[ C C ¨k .E[QE[g C .NG* %E[Q&()*<kgE[©)E7E ¬E[QX)* E C F©E[QFPh C FGD*'XX.NT)E7E h)*R7EFTE 5)*P* ?d-( ij(PaX|IE .E C C H)**Q=()Q 5)EP_Qd-Z)]E[WH(')**gE Pa';)*Ph C "[5)*F)!=()!R)*&(5)*Pa"E[5 C =()!*Ph7¨ C F PaF 'P D* F 5)*Pa g[ ;¬HI E[QE)* C &() ?E[][ &([)\[]*)*H\[~ C E C * . N¨HIE'5H'E(Pa)*

λ1

@ ^


e; P F ACRTA P B5XI? ij C *'Pa)* %*')*X' '*F Pa*')*W=() [dkkjg~Ph)*I kj()*wa C F ";¬HIEF k[ C X)* HQH[5 C &( &([ X)* H_ C F [ &([ H C H C E)E7E C C F H7EWdkH C *'Pa)* G*')*X' wk[ .H[h C E') C * & C %[ &([aX)* \ DN C F wE[)*I=()*dk H(PaX?IE .E .-( C * $()W PaX ACHzJ1RT? K @dn ( ¨XXv J(J(J M P_ C E C hE[57H C H C E)E7E C C FTX)* \ DN)*!X?(* .E .-(.N)*R7EF C C C F'E)N( ADC Pa C NPaGF C &Z7E .-()*R7E C %?IDkj C H C H C E)E7E C C Fakj.)*[5-Z? C =(' C Fv VY+Ph C H C H'* C ACHzJ1RT? K @dn ( GXv J(Je M \7EjE[57- H C H C E)E7E C C F H)* '*I=' C E[57gE[IN&( .-(" C * .NWHPaX';\ C F C E)*X)*I\ C F H7E C[<k H(PaX?IE .E .-(E[j C F'E)N" hg[ \7EPa C E[Zkg)EF]wN E[j C .NG* = FN@1AC? Q C F ?HzJ 1AhK @dn(n M gg[INT*[dk E[57Y C E[ ! |=)*(P @dn n E @dn (E[)*hkj)*[5)*F.N C N )*R7E C !?IDkj C E[W\ .DN~Ph)*IQ*[5)* C FhE[YH[5 C & C H C H C E)E7E C j C .NaF FaE[INh(*)-(YE[YH C H C E)E7E C)E7E ( E[IN *T=(' C F (';QE[57 .E[('&([ E[WH C H C E)E7E C )E7E (!)*Ph C F)*R7E .-(.N©\ E[)* kg"PQ'H[ H(PaX|IE .E C Pa C &E[_F C & 5)*Pa _g[ k+YFF'HF©=)*(PH[5 C &( C &hPh)*IY*[5)* C FTX?(* .E C gE[!F C & 5)*Pa g[)*I=()*Y C ~H CC * PaX.N¥F)Ek H C H'* C C E[©H(PaX?IE .E .-( C * Ph)*IhZN C .N w(w C & 7WuH C H C E)E7E C C F ¬ $5')E[)*Pa()*jd-Z)_E[ .=THINGH~] C C F'E)NPh C N)*R7E C *[ Xak H[5 C &( L-G F C H~=()hE[E')*' C Hj C Ph)*(I*[5)* . <=() C \ C H(X)*d-G FFQZN3= FN@1AC? + C F ?HzJ 1AK @dn(n M XIH9? P K @dn(n M C F H C H) C C &E[h .=_HINGHh C C F'E)N ZN ?H9B9F PS ~ C F P/P ?H F GK @dn (^ M RT? ?H K @dn(n @dn(n M ( C F Q1FIH FIRK @dn(n M lg[IN!*[dk E[57lI-Z C C [ &([.NH C H C E)E7EF] C F'E)N E[H(PaX?IE .E C?IDkj C E[5)*Pa X5)E H'R)*.NE[_F C &5)*Pa H C ?_[5)*Fv XIH9? P K @dn(n M * C FE[57Y C C E)*X)* C ')* RlEH\[ C ((&( H)*&( PagE[!E')*' C HE C FE_?"[ &([v

OG C HE[YH C H C E)E7E C Pa*')*+ C .NG*F?d-Z)*\7E HwE[INa C .N_X)*<-G F C =()*Ph7E . C ?(';E[+F E)E .';\ . C !5)*P* + C E[g C F'E)N( g[IN F C dkH C H'* C % C E[gH(PaX?IE .E .-( C * 7EGF F F P J K J c(c(c Xv @ U M \7E%E[57 / C HY .+ ¨X?(** EQ[5-(YDk+Q C F'E)* ¨k .E[W F C E H|H C H C E)E7E C )E7E (';-()NF Z;¬I)E C C \ DNh C F H 5 C FE C H"\ .DNh*'&(&(EE[ X)** C HYH('* C E[ C \ . .DN C F HX;E')*a C PaX?)*\ C *X?HIaH(PaX?IE E C 3g[h C \ DN~ C F !X)*(X?(*F ZN Z ?H C F9F ACQSA FIB\K @n ZJ M

@ ^ n


g[IN©)*&('"E[57 |=() C \ C H|E[Q C .NG* E[]H\[5 C &(] C )E C E[]FG C & 5)*Pa ?E[]E<DHFE') C <-()Pa*')*¬Fw C HX;E')* C NTH C (Pa H N C E)*E C &! C =()*Ph7E . C `)E H'R)* N 5)*P* Y C jw'5.N F E)* ';EF ZE[Pa*')*gH C \ C C C =()*Ph7E . C 7 "Pa*')*+E[gH(PaX|IE .E .-Z C *%|E[ C F'E)N Z ?Hu C F /F ACQSA F1B K @dn ZJ M '*E[ H\[5 C &( C Ph)*(gE[57)E<-()E["H')E*"7E Pa S )*I*[5)*)* '*F C EF)E C wg?H'*]QPh)*(I*[5)* _.k+dNG_)*R7EF EuE[* E[Ph)*(Ia C FH C E[)*I=()*X)*<-G F C =()*Ph7E . C ?(';!E[aFI-Z(XPa C ]+E[hPh)*I g[W\ DN~ C F E[INX)*(X?(*" gF C F©

I =∑

i∈Zt

(|sit − si,t−1|) ,

k[)*sit C F

si,t−1

)*E[©Ph)*IW*[5)*W 5)*Pi C X?)* wF

t C F

t − 1

)**X?HIE .-(.N( Zt

aE[©*I"HIE .-( 5)*Pah C X?)* wFt g[©\ DN C F

Pa*')*"F )*HIE.NTE[_H\[5 C &(_ C Pa)*(I"*[5)* _g[a C F u C H)**"k .E[E[ C 'PQ?)! 5)*Pa! C H'FIFv A + .! ]**'PaF E[57!E[hFF .E C 5)*Pa!)**Ph Ë[TPa*')*T C W";¬HIEFE &()*7h GE C S ()*d-() gE[ a C F **'PaË[57¨\[&()*<kgE[h)E7E 5)*Pa¨F Z;¬)* C +* j kj &([ZEFWw'5.N( HH(' C =()+E["F Z;¬)* C *(';E -7'HX .\HH'PQ'R7E C E[IN*'&(&(E 'EE[ Ph)*(Ig*[5)*"7gE[ ?& CC C & H\[X?I)E .GF+k+ &([Z %g[ gFE E[ =(dk C & PaGF 5F\ .DNh C F ¬

I =∑

i∈Zt

(|sit − si,t−1|) · si,t−1.K=U KJ M

OG C H+ C E[+* P 'R7* C PaGFGE[+&()*dkgE[ )E7E?*Ph 5)*Pa%)*+'*'5.N!R)*&()E[5 C E[(*¨;R)*&( 5)*Pa <E[PaGF 5F"\ DN C F !l&( .-( C C L%w'57E C K=U KJ M XX F]E"HHI(' C =()E[*gF Z;¬)* C H g[g)**'.E%)*+*[dk C C $ &(')*jU KJe; ADC E[g|&( CC C & 7E[g;¬HIE%? C F'EPa C %X)*GH*¨7)E¨-G * g[g\ .DN C F W ¨-Z)Nh-((R7E .Y C F .EjPad-ZPa C +?H(Pa+*PaGE[)¨=)*(PX?)* wF

t = 10 C ADC |=(')+H* E[\ .DN_FH)** C E C F C HIN k[)*"X57)*E HI'R)*.N_ CE[ 5)*Ph)*IX[5* E[)*" g*(Pa E')*' C H" C E[" C F ¬ g[Ï-(ZGE[\ .DNY C F -)* C E[%=(')lH* C -Z)E&(<E[dkjI-(¬ j(;\ C FW C H* A K c eUw^ M H* A*A K c U(Uw( M H* A*AA K c K^ @ U cNM g[

#"sbVa$cp Va%qscu!a1f7Vp `!d rVp d a%n'$i#. . .V~

@ c


0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5x 10

−3 λ0=0.4, λ

1=0.2

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5x 10

−3 λ0=0.6, λ

1=0.4

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5x 10

−3 λ0=0.8, λ

1=0.6

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5x 10

−3 λ0=0.8, λ

1=0.2

Pa C · · · EF$ &(')* U KJe;¨Ow\ DN ADC F

@ @

U U OG'PaPh)N A RF P ACJ1B

Pa C gH* A c e(ZJ c C F " C E[a)E C &(hgH* A g[)*I=()*%H)X?(* .E .-(T PaX57HIh E[©*)*H\[ C E C * . N¥E[~HIE'5H'E(Pa)*

λ1g C E[

-Z)E&("\ DNh C E["Ph)*IH C ?"(*)-(Fv g["Pa C glE[ \ .DNa C F )*F .-G FF C EQE[E[)* Ph)*IX[5*)*X)** C EF C Ü; KJ(JG ADC X[5* A E[¨()*F))*Ph C E[ËPajl=()E[jP_ C ?E[ C F ¬ g[57¨ (E[ C F %Ph C .N]X|(* .E .-Z.N] C O ' C HFawN

λ1 ADC X[5*

A*A vE[adkj"-'!)*_E ;7 C F C H* A C F A vk[)*λ1 "dkj

ADC H* A*A C F A*A*A E[Q-' )* * Pa .R7) g[ C O ' C H λ1[5 FIH)**F

';a~E)* C &() ;¬HIaE[*)*H\[¥ C E C * .DN E[X|E C E RjH C *'Pa)* λ0

H CC ?"=(' C Fv ADC X[5* A*A*A E[)*])*"(;\ C F* Pa )j-7'=()Pa(H* C .N C H* A . C E HE[57E[! &_F Z;¬)* C H]|I kj C

λ0 C F

λ1*PagEa C H)**"E[" C *\ . Nh C E[57Ph)*I

U KJ(JGÖw\ N ADC F a`%[5*

b`%[5* A `%[5* A*A `%[5* A*A*A

i+*i+* A c UZZJe c e((e( c KJ @(@ Ji+* A*A c ZJ( c UZUwJ c KJeZJ7Ui+* A*AA c UZ n c Uw n(c c KJ @ e ni+* A c UZ c e c e(Z7U c KJ((ea"sbVa $cp Va%q/cu!aIf7Vp `!d rVp d a%n $ i#. . .V~

bb"cqwa%q #B' ##B'zce"n ###jk#_#$auh`!bVa)rtau!d _onVq

t = 1`!_ *.'

t = 34`!_ Y*Y.'oce"n

t = 67`!_E>*>V~

>( 4 .

g[ C .NG* W!E[~F57\ *[dkE[57E[~FI-((XPa C "E[u* PQ'R7EF C F'E)NFX? C F C E[ *7)EH\[HIE .-G .E j7lE[ H C *'Pa)* ;k .E[WE[E)*H[ C E C * .E jlE[X?E C E RvH C *'Pa)* C FE[!HIE'5H'E(Pa)*XRNG C & F Z;¬)* C )*( ij C H) C C & 5)EhE[ 5)*PbH\[5)EHIE)* E H &( C )EYX57*E) C hI-G F C 3$5()aPa(Ë[ -7)E * ¬E[5)*P* lX)* E! C FuX?)=()*Ph C H C -(EPa C C F ;X? C F .E')* E[a*)*H\[ C E C * .DN~+E[aX?E C E R%H C *'Pa)*

λ0";¬HIE!E[aI-(

lE[Pa C ;k[)*+E[*)*H[ C E C * .DNhlE[ HIE'5¬H'E(Pa)* λ15HH(' C E+=()

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.Eg-)* R . N A =()gE[]|<-(DPa C E C F-)* RgE[57Y C C H)**!E[!Pa C &( C )E.Nh=(.dk+FZN .EgFH)** +g[![ &([)

λ0 E[![ &([)g gE["Pa C ¨g[

\ C F5)*FhFI-G R7E C [ &([_=()[ &([λ1 A j C .NQ=()%E[X)* E¨ C FaE[X?)=()*Ph C H

E[57E[%\ C F5)*F!FI-G R7E C FH)**d-()E[%H(')**GE Pa lg[[ .&([)vE[%)E C F(P;¬HI¨H'*FaZN_[ &([ *)*H[_ C E C * .DNQ7?E[gX?E C E R;H C *'Pa)* ZE[g[ &([))*g Cd-()E&(?E[WE[HX .\?EGH\W C FWE[X)* EgE[ 5)*Pa ADC -ZEPa C C HX .\¬k+I ;X? C F .E')*Y C *_ C H)**] C d-()E&(! .E[]HIE'5H'E(Pa)*E C FE )*Ph C dNZ+EuE[ ) 5)*P ¥g[TPh C )** C k[ZN C E C * .-(.N *)*H\[ C & HIE'5H'E(Pa)*k F C E["F Z;¬)* C HYPa C &5)*Pag*PaE_? E[57E["X)***')*] ;)EF C 5)*Pa )EIR7E .-Z.N [ &([ 7k[ H\[QX)E-Z C E 5)*Pa=)*(P3X?)=()*Pa C &k+G C H(PaX|IE .E C A ]E[ HIE'5 H'E(Pa)**)*H[ k \[dk C E C * .DN 5)*Pa C &Z&(u C X C & E[ )H'E(Pa)* C F 7*E)EHIE C & H'E(Pa)*=)*(P,E[ )H(PaX|IE .E()* C ()*F)WE¥H)*7E 5* ]=()>K9=')E[) M &()*<kgE[v ©g[)*I=()*%E[-()E&(W ;X? C F .E')* C C H)** C

λ1 ADC E)*E C &(.N ? .E[Q*)*H\[~ C E C * .DN%E[QHIE'5H'E(Pa)*

λ1? Y[ &([ 5E[

C 'PQ?I) Pa \7E . C Y C F~ CC d-77E C Y Ydkj)E[5 C .λ1 Ydk ¬ * ?F*X .EQ[ &([)

;X? C F .E')* E[ *(';E C 'P |)gl Pa .\<E . C + C F CC d-7E C +jkjv+E[H()*F'HIE C C F'HFZNhE['E&( C IkEH[ C ((&( +)*Y<kj) %$5()+?H C ER7E C

λ0 C F

λ1?E[ d-()E&(QX)*GF'HIE C H(E FIH)**_EF .N( VY.E[('&([TE[)*Q C

(w-G .(' C O ' C H]E[!*)*H[© C E C * .E \[!dkj)?(' C FTE[!X)*GF'HIE C H*E g)*H[IFT)* )+ .

λ1 g<k"

S ()*<-() (E[+ C .NG* *[dkE[57*Ph 5)*Pa&()*dk E)% C FQ C -(YR)*&()Pa(' C lPa C INaX?)j' C .+lHX .\5E[5 C R)*&(5)*Pa ¨OGPh)5)*Pa+*][5d-([ &([)¨ ;X? C F E')*+ C X?I)+' C .jHX .\ ;X? C F .E')* K9E\? C FWX|)j' C .jHX .\ M)*u* &([ZE.N C &Z7E .-(.NH()*)*R7EF k .E[5)*P * C F =)*(P X[5* A*A C E[IN)*C &Z7E .-(.NTH()*)*R7EF©k .E[~X)* E ]OGPh/5)*Pa F' Pa()*Qw' H\w.NEWE[ FPh C FH C F .E C E[5 C R)*&( 5)*Pa l)*&( 5)*Pa)*&( C )E.N H\[5)EHIE)* FQZN! C ;H**'XGX.N( A %E[]*)*H\[~ C E C * .DNE[QHIE'5H'E(Pa)*Y Y[ &[ |E[QF'EPa C YX)*GH* +E) `%)* H!)*HI]F Z;¬)* C E.N~ C ?E[ E)*H[ HIE .-G .E lFX| C F C &T C E[aX[57EajE Pa ADC E)*E C &(.NE[-()E&(WX)* HQ C H)**WF')* C &E[ 5)* X[5* C F FH)** C .N79E)*(PagE Pa+[5¨X5**Fv %g[\ C F5)*FaFI-G R7E C )*Ph C %)*R7E .-(.NQH C \ C j C F [ &([)%=()R)*&(+-'

λ0 ADC E[X[5* A C F A*A w![ &([a-Z)E&(X)* H Ph C N

H'*FWZNλ0wk[)*j C E[R¨X[5*wE[-()E&(X)* HFX| C F C &Z7E .-(.N C

λ1

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A ¬7*E C E C E') C F EYE[+Ph)*(IE)*'HIE')*ZE[+ C O ' C H+?|E[ *)*H\[_ C E C * .E -)* ¨g[ C 'PQ?)5)*Pa C E[!Ph)*IFX| C F C &Z7E .-(.N C

λ1| C FE[!\ C

F5)*FuFI-G 7E C * &[wE N C &Z7E .-(.NT)*R7EF©Eλ0 !g[ C 'PQ?)¨ C E)* FX? C F

C E[!E Pa [()* C j C E[!*[())*' C | E 5 C E[5)*X[5*|E[ C 'PQ?)% C E)* Y[ &([)=()Y[ &([

λ0 ADC E[Q C &h)*' C ?E[ C &Z7E .-Z] C O ' C HQ

λ1 X)*F(Pa C C d

g[Q5 C w)*'X;EHINT)E7E!FH)** C lH*d-()E[]H(')**QE Pa! C FT R)*&() Cd-()E&(jk[)*

λ1 R)*&( ij C H) C C &E[g ;X|HIEFa .=IE P_¨!5)*Pa 5)*PaE[57 C E)

E[!Ph)*IY7YaR<\I)X?( C 7E Pa .-Z C &()g C -()E&("E[5 C E[" C H'P | C E';[5d-(! <kj)gX?)=()*Ph C H g[ 5)*P D* F E)* ';E C E[57_Pa)*&( =)*(P E[* PQ'R7E . C (& C ()*Ph V dk*)*H[ C E C * .DN!\[ HIE'5 HI'*E(P_)*

λ1 XX|)*E ?~E[uPa( .PaX?()\ C

X5)EPaIE)!E©*'XX?()QE[W&()*dkgE[ 5)*Pa ©g[NGPaPaIE)* H 5)*P D* aF \)* ';E C aHH(PaX5 C F¥ZN¥uEF .N C H)** C & ) C F5[ C F ¥H C H C E)E7E C C E[Ph)*(d Wg[WHI C H C E)E7E C "X?(* .E .-(.Nu";¬HIEF wN [ &([ *)*H\[ C E C * . N~+E[HIE'5wHI'*E(P_)*

λ1 ij(PaX5)* C &gE[¨) C F5[G C F k .E["E[¨\ NY C F !*[dk

E[57\["H C H C E)E7E C H()*)**X? C FEaPh)*IX?dk+) C FFv ADC E[5)*YX[5*|E[\ .DN C F Q)*R7E .-Z.N [ &([ C F E[Ph)*I_*[5)* ;[ . *(PaWE')*' C H Y-ZI)QE[H(')**E Pa[dkjI-Z) E[W\ .DN C F FH)**h7QE[I) C F57[ C F ~ C H)** Q+[ Pa C E[57E[ Ph)*I"*[5)*")* )*R7E .-(.N\ *WE[57![ &([aH C H C E)E7E C C F a w' .- C ¨E!dkH(PaX?IE .E C Pa C & 5)*Pa ADC E[*[())*' C E["\ .DNh C F gX|(* .E .-Z.NW";¬HIEFwN

λ1

S (hYE[DNG F¥HIE_Pa C E C F C E[?&( CC C &uH C |)*X)*GF'HFZN E[* P '7E . C F57\; g[¨H C H C E)E7E C C H)**<-()lE[¨H(')**j;E Pa7 C F"\[Ph)*(I*[5)*]|H(PaaPa()* \ hg[ 5)*P D* F E)* ';E C !NGPaPaIE)* H_ C F \ k+IE~(& C ()*Ph7%F E)* ';E C V C F;- C \&(h 5)*P * h C H CC ]?a=(' C F C F©E[QDNG FTHIEH C H) C C &WE[Q .=DHINGH![ZNGX?E[* H CC "l?QH C 5)*PaF !X)*F HIEFu=()"[(Pa(&( C ('"&(GGF h+[ C 'PQ?)"+ C E)* ! "EF .N© C H)** C & C F ¬E[)*I=()*?E[ C 'PQ?I) 5)*PaY C E[QPh)*I Yw' .EQ[ &([v I-()E[* l .Y I-G F C jE[57E[F Z;¬)* C HPhF?IDkj C X?E C E R5H C *'Pa)*+ C FhHIE'5|H'E(Pa)* g';EPa( PaX?()\ C H $ C N E[!H C H'* C F)Ek C C * PaX \7E H!*)*H\[©PaGFgE[57Y[ &([*)*H\[~H*EF C H*E)* .NE¥ [ &([Ph)*IX)* H~H CC |u*'\ C F C E[~I-Z';E C )N=)EPaIkj()*| ADC EF ¬ C ][5EWF E C &(' .*[TH)*I='.N?IDk+ C E[]*)*H\[~ C E C * .E

@ U


YX?E C E R+H C *'Pa)*h C F¥HIE'5gH'E(Pa)* ¥$5')E[)*Pa()*¨ C [5a*©Eu\ C E"HH(' C ¨E[)**X?HIE .-(Ph)*I¨X[5*|H'*E[;¬HIE¨?E[*)*H\[h|[5d-G (')+|E[ &()*('X"FX? C F C E[_FI-((XPa C !jE[_ C F'E)N©k .E[u)**X?HI!E .E .=HINGH

@ Z^

A cynic is a man who loves the price of everything and the valueof nothing. s % "&

g[ PE[ Ë[* ¨k+jEQFPa C E)E7EYE[57+H C *'Pa)* ;?[5-G (')j[5g]FH * .-( PaX5HI] C E[W CC d-7E .-(h|[5d-G (')] 5)*Pa C F C E[WFI-((XPa C C F'E)N( VYQ=)EPaIkj()* ;E[ I-Z(';E C )Nh* PQ'R7E . C PawFvE ACB P ?H K @dn U M k+H\[(* C g[ ! C aË[(*aPaGFE[57"=(dk E[hOGH[w'PaX?IE)* R C XX)*ZH\[ C F E[57!)*HX5Y7lHX;E')* C &] PaX|()\ C %=7E')*+' C F)*.NG C &!E[YX)*GHIE+H C (Pa HH\[5 C &( ij(PaX5)*F_E"E[()E[GF C GHR** H5PaGF%H C H) C C &!EH\[ C ((&( HH\[5 C &(wE[I-Z';E C )NWXX)*ZH\[[5g*I-()ElF;- C \&( ¨$ )* G .+(X?)E7E+k .E[(';gH C E)*'HI C &EF;N \7E Wij C *w' C E.N Ph C N~H C E)E C C &**'PaX;E C E[57" C *')E_E[ ; E C Hl C w' )* 'PH C ?5 C F C Fv ÖGHI C F C H C F!k .E[(';Ë[YH C E)*<-()** Rj**'PaX;E C )E7E C ;X?HI\7E C ~g[ )*F . dk"=()][IE)*(&( C ('H C (Pa H &( C E C EFu¨ C )*X)** C \7E .-(a&( C Q$ C N ?E[ I-((';E C )N©XGX)*ZH\[dkE C .NG*X)*wH** C )*?E PaY C F ;[ C Ht;¬)*g C ;XR C 7E C =()E["PaH\[5 C *PagE["F)* .-G C & =()*HH C (Pa HH[5 C &( g[Ph()H[5 C &(YX?)=()*PaFW C E[ E[* + ËQ GE C FWE[Y=GH'j C I-Z';E C )N* P '7E . C PaGFEdk+)*FT)*&Z7)EF C & E[ H C (P]N T k[( C .N HI7C (Pa H"X)*(&()**YH C E C & C Y C CC d-7E .-(5)*Pa | .*aFX? C F C E[]?I[5d-G (')H C *'Pa)* ADC H C E)E"EE[a()E[GF uPh)*I!PaGF H C *'Pa)*Q)*_ PaX?)=HIE.N C =()*PaF© C F~[5-(QEW C &Z&(] C H(E.NT*)*H\[~=)W*'XX ) L%w'5.N +5)*PaYH CC ? *')* E *?E[ )+&(GGF C H)5)*PagPQ' C &Z&( C H()*F'H C &aHIE .-G .E * v C ¬E&( C )E7E X)*GH*" CC <-77E C ()Y\ Pa \7EQX)*GF'HIE C EH\[ C w'+H(PaX?\ \) ¬k[ H\[ [X"(X C &E[_(';EX';!X)* H dk C F &Z C C &H'E(Pa)* g[ "X)*GH*! C &(( C &|H'*aH C *'Pa)* C I-()!E(X *)*H\[ C & _g[(* k[[5-Z

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