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Index
Bridge: Bessel - 1-36, II-15 Brownian - 1-2, II-18
pseudo- - 1-125
Brownian motion: perturbed - II-129 randomized - II-91 skew - 1-99 Walsh - II-I07
Chaos: Wiener - I-I Wiener - decomposition 1-27
Decomposition: canonical - II-34
Doob-Meyer - 11-65 non-canonical- 11-118 semimartingalc - 1-47
Decomposition of paths: Vervaat - II-17 Williams - II-33
Distribution: Arc sine - 1-99, 11-9 Beta - 1-100
Gamma - 1-100 Hartman-Watson - 1-61
Enlargements of filtrations: initial - II-33 progressive - II-41
Equation: conditional - II-73 Langevin's - 1-11
142
Skorokhod's reflection - 1-116
structure - II-102
Equivalence:
Levy's - 11-78
past and future - II-113
Excursion: Ito's - measure 1-30
Master formulae of - theory 1-30
- measures 11-15
normalized Brownian - 11-14
- theory 11-9
Filtration:
Brownian - II-117
Goswami-Rao - 11-115
Formula: agreement - II-14
balayage - II-61 Feynman-Kac - 1-86
integration by parts - I-53 Ito's - II-58
Levy's stochastic area - 1-16
Tanaka's - 1-107
Function:
confluent hypergeometric - 1-48 gamma - II-12
moderate - II-51
modified Bessel - 1-60
non-moderate II-54
Riemann zeta - 11-11 theta - 11-11
Young - II-54
Functional:
additive - 1-121,11-7
Brownian - 1-15
- equation 11-11
quadratic - 1-18
skew-multiplicative - 1-31
Identity:
Chung's - II-16
Ciesielski-Taylor - I-50
Jacobi's - 11-12
Knight's - 1-124, 11-19
Kolmogorov-Smirnov's - 11-16
Index:
- of a Bessel process II-26
- of a stable process 11-4
Inequality:
Burkholder-Gundy - II-51
Fefferman - II-57
Hardy's - 1-9
Information:
loss of - 11-114
Integral:
multiple Wiener - 1-15, II-81
stochastic - 11-32 stochastic - representation 11-104
Intertwining: 1-74,1-84, II-88
Lace: Brownian - 1-64
Lemma:
Jeulin's - 11-39
"Poincare's" - II-55
Levy:
- equivalence 1-102, 11-78
- exponent 1-71
- measure II-40
- process 11-35
INDEX
Local times: Brownian - 1-27
intersection - 1-95
Martingale: Azema's first - 11-80 Azema's second - 11-80 BMO- - II-58 Emery's - 11-87
parabolic - 11-88
spider - 11-109
Meander: Brownian - 1-41
generalized - 1-41, II-127
Norm: Luxemburg - II-54 Orlicz - II-54
Number: Gauss linking - 1-87
self-linking - 1-94
winding - 1-88
Occupation:
density of - formula 11-49 - measure 1-12 - times formula 1-27
Options: Asian - 1-68, 11-128
Polynomials: Hermite - II-82
Laguerre - 1-5
Principle: transfer - 1-27, 1-35
Process: Bessel - 1-28 Cauchy - 1-64, 11-39 Dirichlet - II-3 increasing - II-65
143
144
injective - II-72 Levy - 1-75
optional - II-62
Ornstein-Uhlenbeck - 1-16 predictable - II-62
progressively measurable - II-62
stable - II-40
Property:
regeneration - II-75
scaling - II-20, II-34
strong Markov - II-24
Quantiles: Brownian II-128
Relation: Imhof's - 1-42, II-44
Representation: Ito's martingale - II-62
Lamperti's - of a semi-stable Markov process II-93
Pitman's - of the BES(3) process 1-28, II-118
stochastic integral- II-83, II-104 Vervaat's - of the Brownian
excursion II-16
INDEX
Reversal: time - 1-28 Williams' time - II-36
Semimartingale: 1-3 - decomposition 1-47
Set: end of a predictable - II-108
saturated - II-107 Sheet:
Brownian - II-126
Snake: Brownian - II-75, II-128
Space-time: - harmonic function 1-9, II-121
Supermartingale: Azema - II-41
Supremum:
- of Brownian bridge II-16 - of Brownian excursion II-16 - of Brownian motion 1-102
Theorem: Knight's - 1-107
Time: random - II-41, II-52 stopping - II-41
PROBABILITY THEORY • STATISTICS
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Some Aspects of Brownian Motion Part I: Some Special Functionals
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Birkhäuser Birkhäuser Verlag AG Basel ' Boston ' Berlin
PA • Probability and Its Applications
A. Borodin, St. Petersburg, Russia / P. Salminen, Abo Akademi University, Turku, Finland
Handbook of Brownian Motion Facts and Formulae 1996. 476 pages. Hardcover ISBN 3-7643-5463-1
The purpose of this book is to provide
an easy reference to a large number of
facts and formulae associated with
Brownian motion. The book consists
of two parts. The first part, dealing
with theory, is devoted mainly to pro
perties of linear diffusions in general
and Brownian motion in particular.
Results are given mainly without pro
ofs. The second part is a table of dis
tributions of functionals of Brownian
motion and related processes. The
collection contains more than 1500
numbered formulae.
This book is of value as basic reference
material for researchers, graduate stu
dents, and people doing applied work
in Brownian motion and diffusions. It
can also be used as a source of expli
cit examples when teaching stocha
stic processes.
For orders originating from alt aver the wortd except USA and Canada: Birkhäuser Verlag AG P.O Box 133 CH-4010 Basel/Switzerland Fax: +41/61/205 07 92 e-mail: [email protected]
For orders originating in the USA and Canada: Birkhäuser 333 Meadowland Parkway USA-Secaurus, NJ 07094-2491 Fax: + 1 201 348 4033 e-mail: [email protected]
VISIT DUR HDMEPAGE http://www.birkhauser.ch
Birkhäuser Birkhäuser Verlag AG Basel ' Boston' Ber lin