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Bibliography of Jim Pitman arranged by subjects inalphabetical order

April 25, 2003

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Contents

Abel-Cayley-Hurwitz multinomial expansions

[1] J. Pitman, “Random mappings, forests and subsets associated with Abel-Cayley-Hurwitzmultinomial expansions,”Seminaire Lotharingien de CombinatoireIssue 46(2001) 45 pp.,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[2] J. Pitman, “Forest volume decompositions and Abel-Cayley-Hurwitz multinomialexpansions,”J. Comb. Theory A.98 (2002) 175–191, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Additive coalescent

[1] R. Sheth and J. Pitman, “Coagulation and branching process models of gravitationalclustering,”Mon. Not. R. Astron. Soc.289(1997) 66–80, Preprint [.ps.Z].

[2] S. Evans and J. Pitman, “Stationary Markov processes related to stable Ornstein-Uhlenbeckprocesses and the additive coalescent,”Stochastic Processes Appl.77 (1998) 175–185,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] D. Aldous and J. Pitman, “The standard additive coalescent,”Ann. Probab.26 (1998)1703–1726, Article [.pdf], Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

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[4] J. Pitman, “Coalescent random forests,”J. Comb. Theory A.85 (1999) 165–193, Article[.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[5] D. Aldous and J. Pitman, “Inhomogeneous continuum random trees and the entranceboundary of the additive coalescent,”Probab. Th. Rel. Fields118(2000) 455–482, Article[.pdf], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Additive functionals

[1] P. J. Fitzsimmons and J. Pitman, “Kac’s moment formula and the Feynman-Kac formula foradditive functionals of a Markov process,”Stochastic Process. Appl.79 (1999) 117–134,Preprint [.ps.Z], Article [.pdf], ScienceDirect, Math. Review.

Amplitude

[1] J. Pitman and M. Yor, “Path decompositions of a Brownian bridge related to the ratio of itsmaximum and amplitude,”Studia Sci. Math. Hungar.35 (1999), no. 520, 457–474,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Appell’s hypergeometric functions

[1] M. E. H. Ismail and J. Pitman, “Algebraic evaluations of some Euler integrals, duplicationformulae for Appell’s hypergeometric functionF1, and Brownian variations,”Canad. J.Math.52 (2000) 961–981, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Arcsine laws

[1] M. Barlow, J. Pitman, and M. Yor, “Une extension multidimensionnelle de la loi de l’arcsinus,” inSeminaire de Probabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 294–314.Springer, 1989. Math. Review.

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[2] J. Pitman and M. Yor, “Arcsine laws and interval partitions derived from a stablesubordinator,”Proc. London Math. Soc. (3)65 (1992) 326–356, Math. Review.

[3] J. Pitman and M. Yor, “Some properties of the arc sine law related to its invariance under afamily of rational maps,” Tech. Rep. 558, Dept. Statistics, U.C. Berkeley, 1999.Abstract[.txt], Preprint [.ps.Z].

Associahedron

[1] J. Pitman and R. Stanley, “A polytope related to empirical distributions, plane trees, parkingfunctions and the associahedron,”Discrete and Computational Geometry27 (2002) 603–634,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Asymptotic laws

[1] J. Pitman and M. Yor, “The asymptotic joint distribution of windings of planar Brownianmotion,” Bulletin of the American Mathematical Society10 (1984) 109–111, Math. Review.

[2] J. Pitman and M. Yor, “Asymptotic laws of planar Brownian motion,”Annals of Probability14 (1986) 733–779, Article [.pdf], Math. Review.

[3] J. Pitman and M. Yor, “Complementsa l’etude asymptotique des nombres de tours dumouvement brownien complexe autour d’un nombre fini de points,”C.R. Acad. Sc. Paris,Serie I 305(1987) 757–760, Math. Review.

[4] K. Burdzy, J. Pitman, and M. Yor, “Some Asymptotic Laws for Crossings and Excursions,” inColloque Paul Levy sur les Processus Stochastiques, Asterisque 157-158, pp. 59–74. SocieteMathematique de France, 1988. Math. Review.

[5] J. Pitman and M. Yor, “Further asymptotic laws of planar Brownian motion,”Annals ofProbability17 (1989) 965–1011, Article [.pdf], Math. Review.

[6] M. Klass and J. Pitman, “Limit laws for Brownian motion conditioned to reach a high level,”Statistics and Probability Letters17 (1993) 13–17, Math. Review.

[7] M. Camarri and J. Pitman, “Limit distributions and random trees derived from the birthdayproblem with unequal probabilities,”Electron. J. Probab.5 (2000) Paper 2, 1–18, Article,Math. Review.

3

Asymptotic speed

[1] D. Aldous and J. Pitman, “The asymptotic speed and shape of a particle system,” inProbability, Statistics and Analysis, London Math. Soc. Lecture Notes, pp. 1–23. CambridgeUniv. Press, 1983. Math. Review.

Asymptotics of combinatorial structures

[1] D. Aldous and J. Pitman, “Brownian bridge asymptotics for random mappings,”RandomStructures and Algorithms5 (1994) 487–512, Math. Review.

Bayesian inference

[1] B. Hansen and J. Pitman, “Prediction rules and exchangeable sequences related to speciessampling,”Stat. and Prob. Letters46 (2000) 251–256, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Bessel bridges

[1] J. Pitman and M. Yor, “A decomposition of Bessel bridges,”Z. Wahrsch. Verw. Gebiete59(1982) 425–457, Math. Review.

[2] J. Pitman and M. Yor, “Sur une decomposition des ponts de Bessel,” inFunctional Analysis inMarkov Processes, M. Fukushima, ed., vol. 923 ofLecture Notes in Math, pp. 276–285.Springer, 1982. Math. Review.

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Bessel functions

[1] J. Pitman and M. Yor, “The law of the maximum of a Bessel bridge,”Electron. J. Probab.4(1999) Paper 15, 1–35, Article, Math. Review.

Bessel polynomials

[1] J. Pitman, “A lattice path model for the Bessel polynomials,” Tech. Rep. 551, Dept. Statistics,U.C. Berkeley, 1999. Abstract[.txt], Preprint [.ps.Z].

Bessel process

[1] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[2] J. Pitman and M. Yor, “Processus de Bessel, et mouvement brownien, avec drift,”C.R. Acad.Sc. Paris, Serie A291(1980) 151–153, Math. Review.

[3] J. Pitman and M. Yor, “Bessel processes and infinitely divisible laws,” inStochastic Integrals,vol. 851 ofLecture Notes in Math., pp. 285–370. Springer, 1981. Math. Review.

[4] J. Pitman and M. Yor, “Quelques identites en loi pour les processus de Bessel,” inHommageaP.A. Meyer et J. Neveu, Asterisque, pp. 249–276. Soc. Math. de France, 1996. Math. Review.

[5] J. Pitman and M. Yor, “Random Brownian scaling identities and splicing of Besselprocesses,”Ann. Probab.26 (1998) 1683–1702, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

[6] J. Pitman and M. Yor, “The law of the maximum of a Bessel bridge,”Electron. J. Probab.4(1999) Paper 15, 1–35, Article, Math. Review.

[7] M. Jeanblanc, J. Pitman, and M. Yor, “Self-similar processes with independent incrementsassociated with Levy and Bessel processes,”Stochastic Processes Appl.100(2002) 223–232,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

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Bessel processes

[1] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[2] J. Pitman and M. Yor, “Bessel processes and infinitely divisible laws,” inStochastic Integrals,vol. 851 ofLecture Notes in Math., pp. 285–370. Springer, 1981. Math. Review.

[3] J. Pitman and M. Yor, “Quelques identites en loi pour les processus de Bessel,” inHommageaP.A. Meyer et J. Neveu, Asterisque, pp. 249–276. Soc. Math. de France, 1996. Math. Review.

[4] J. Pitman and M. Yor, “Random Brownian scaling identities and splicing of Besselprocesses,”Ann. Probab.26 (1998) 1683–1702, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

[5] M. Jeanblanc, J. Pitman, and M. Yor, “Self-similar processes with independent incrementsassociated with Levy and Bessel processes,”Stochastic Processes Appl.100(2002) 223–232,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Birth and death chains

[1] H. Dette, J. Fill, J. Pitman, and W. Studden, “Wall and Siegmund duality relations for birthand death chains with reflecting barrier,”Journal of Theoretical Probability10 (1997)349–374, Preprint [.ps.Z], Math. Review.

Birth times

[1] M. Jacobsen and J. Pitman, “Birth, death and conditioning of Markov chains,”Annals ofProbability5 (1977) 430–450, Math. Review.

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Birthday problem

[1] M. Camarri and J. Pitman, “Limit distributions and random trees derived from the birthdayproblem with unequal probabilities,”Electron. J. Probab.5 (2000) Paper 2, 1–18, Article,Math. Review.

Branching processes

[1] J. Neveu and J. Pitman, “The Branching Process in a Brownian Excursion,” inSeminaire deProbabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 248–257. Springer, 1989. Math.Review.

[2] R. Sheth and J. Pitman, “Coagulation and branching process models of gravitationalclustering,”Mon. Not. R. Astron. Soc.289(1997) 66–80, Preprint [.ps.Z].

[3] D. Aldous and J. Pitman, “Tree-valued Markov chains derived from Galton-Watsonprocesses,”Ann. Inst. Henri Poincare34 (1998) 637–686, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[4] J. Pitman, “Enumerations of trees and forests related to branching processes and randomwalks,” in Microsurveys in Discrete Probability, D. Aldous and J. Propp, eds., no. 41 inDIMACS Ser. Discrete Math. Theoret. Comp. Sci, pp. 163–180. Amer. Math. Soc.,Providence RI, 1998. Abstract[.txt], Preprint [.ps.Z], Math. Review.

[5] J. Bennies and J. Pitman, “Asymptotics of the Hurwitz binomial distribution related to mixedPoisson Galton-Watson trees,”Combinatorics, Probability and Computing10 (2001)203–211, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Bridges and excursions

[1] J. Pitman and M. Yor, “Decomposition at the maximum for excursions and bridges ofone-dimensional diffusions,” inIto’s Stochastic Calculus and Probability Theory, N. Ikeda,S. Watanabe, M. Fukushima, and H. Kunita, eds., pp. 293–310. Springer-Verlag, 1996. Math.Review.

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[2] J. Pitman and M. Yor, “The law of the maximum of a Bessel bridge,”Electron. J. Probab.4(1999) Paper 15, 1–35, Article, Math. Review.

Brownian bridge

[1] J. Bertoin and J. Pitman, “Path Transformations Connecting Brownian Bridge, Excursionand Meander,”Bull. Sci. Math. (2)118(1994) 147–166, Math. Review.

[2] D. Aldous and J. Pitman, “Brownian bridge asymptotics for random mappings,”RandomStructures and Algorithms5 (1994) 487–512, Math. Review.

[3] J. Pitman, “The SDE solved by local times of a Brownian excursion or bridge derived fromthe height profile of a random tree or forest,”Ann. Probab.27 (1999) 261–283, Article[.pdf], Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[4] P. Carmona, F. Petit, J. Pitman, and M. Yor, “On the laws of homogeneous functionals of theBrownian bridge,”Studia Sci. Math. Hungar.35 (1999) 445–455, Abstract[.txt], Preprint[.ps.Z], Math. Review.

[5] J. Pitman and M. Yor, “Path decompositions of a Brownian bridge related to the ratio of itsmaximum and amplitude,”Studia Sci. Math. Hungar.35 (1999), no. 520, 457–474,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[6] J. Pitman, “The distribution of local times of Brownian bridge,” inSeminaire de ProbabilitesXXXIII, vol. 1709 ofLecture Notes in Math., pp. 388–394. Springer, 1999. Abstract[.txt],Preprint [.ps.Z], Math. Review.

[7] J. Pitman, “Brownian motion, bridge, excursion and meander characterized by sampling atindependent uniform times,”Electron. J. Probab.4 (1999) Paper 11, 1–33, Article, Math.Review.

[8] J. Pitman and M. Yor, “On the distribution of ranked heights of excursions of a Brownianbridge,”Ann. Probab.29 (2001) 361–384, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

[9] D. Aldous and J. Pitman, “Two recursive decompositions of Brownian bridge related to theasymptotics of random mappings,” Tech. Rep. 595, Dept. Statistics, U.C. Berkeley, 2002.Abstract[.txt], Preprint [.ps.Z].

[10] D. Aldous and J. Pitman, “The asymptotic distribution of the diameter of a randommapping,”C.R. Acad. Sci. Paris, Ser. I334(2002) 1021–1024, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

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[11] D. Aldous, G. Miermont, and J. Pitman, “Brownian bridge asymptotics for randomp-mappings,” Tech. Rep. 624, Dept. Statistics, U.C. Berkeley, 2002. Abstract[.txt], Preprint[.ps.Z].

Brownian bridges and excursions

[1] J. Bertoin and J. Pitman, “Path Transformations Connecting Brownian Bridge, Excursion andMeander,”Bull. Sci. Math. (2)118(1994) 147–166, Math. Review.

[2] J. Pitman, “The distribution of local times of Brownian bridge,” inSeminaire de ProbabilitesXXXIII, vol. 1709 ofLecture Notes in Math., pp. 388–394. Springer, 1999. Abstract[.txt],Preprint [.ps.Z], Math. Review.

[3] J. Pitman, “Brownian motion, bridge, excursion and meander characterized by sampling atindependent uniform times,”Electron. J. Probab.4 (1999) Paper 11, 1–33, Article, Math.Review.

Brownian crossings

[1] K. Burdzy, J. Pitman, and M. Yor, “Brownian crossings between spheres,”J. of MathematicalAnalysis and Applications148, No. 1(1990) 101–120, Math. Review.

Brownian excursion

[1] J. Pitman and M. Yor, “Ranked functionals of Brownian excursions,”C.R. Acad. Sci. Parist.326, Serie I (1998) 93–97, Article [.pdf], ScienceDirect, Math. Review.

[2] J. Pitman, “The SDE solved by local times of a Brownian excursion or bridge derived fromthe height profile of a random tree or forest,”Ann. Probab.27 (1999) 261–283, Article [.pdf],Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] P. Biane, J. Pitman, and M. Yor, “Probability laws related to the Jacobi theta and Riemannzeta functions, and Brownian excursions,”Bull. Amer. Math. Soc.38 (2001) 435–465, Article,Math. Review.

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Brownian excursions

[1] J. Pitman and M. Yor, “Ranked functionals of Brownian excursions,”C.R. Acad. Sci. Parist.326, Serie I (1998) 93–97, Article [.pdf], ScienceDirect, Math. Review.

[2] P. Biane, J. Pitman, and M. Yor, “Probability laws related to the Jacobi theta and Riemannzeta functions, and Brownian excursions,”Bull. Amer. Math. Soc.38 (2001) 435–465, Article,Math. Review.

Brownian extrema

[1] J. Neveu and J. Pitman, “Renewal Property of the Extrema and Tree Property of aOne-dimensional Brownian Motion,” inSeminaire de Probabilites XXIII, vol. 1372 ofLectureNotes in Math., pp. 239–247. Springer, 1989. Math. Review.

[2] J. Neveu and J. Pitman, “The Branching Process in a Brownian Excursion,” inSeminaire deProbabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 248–257. Springer, 1989. Math.Review.

Brownian meander

[1] J. Bertoin and J. Pitman, “Path Transformations Connecting Brownian Bridge, Excursion andMeander,”Bull. Sci. Math. (2)118(1994) 147–166, Math. Review.

[2] J. Pitman, “Brownian motion, bridge, excursion and meander characterized by sampling atindependent uniform times,”Electron. J. Probab.4 (1999) Paper 11, 1–33, Article, Math.Review.

Brownian motion

[1] J. Pitman, “Path decomposition for conditional Brownian motion,” Tech. Rep. 11, Inst.Math. Stat., Univ. of Copenhagen, 1974.

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[2] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[3] J. Pitman, “Remarks on the convex minorant of Brownian motion,” inSeminar on StochasticProcesses, 1982, pp. 219–227. Birkhauser, Boston, 1983. Math. Review.

[4] J. Pitman and M. Yor, “The asymptotic joint distribution of windings of planar Brownianmotion,” Bulletin of the American Mathematical Society10 (1984) 109–111, Math. Review.

[5] J. Pitman and M. Yor, “Asymptotic laws of planar Brownian motion,”Annals of Probability14 (1986) 733–779, Article [.pdf], Math. Review.

[6] J. Pitman and M. Yor, “Some divergent integrals of Brownian motion,” inAnalytic andGeometric Stochastics: Papers in Honour of G. E. H. Reuter (Special supplement to Adv.App. Prob), D. G. Kendall, J. F. C. Kingman, and D. Williams, eds., pp. 109–116. AppliedProb. Trust, 1986. Math. Review.

[7] J. Pitman and M. Yor, “Complementsa l’etude asymptotique des nombres de tours dumouvement brownien complexe autour d’un nombre fini de points,”C.R. Acad. Sc. Paris,Serie I 305(1987) 757–760, Math. Review.

[8] J. Pitman and M. Yor, “Further asymptotic laws of planar Brownian motion,”Annals ofProbability17 (1989) 965–1011, Article [.pdf], Math. Review.

[9] M. Barlow, J. Pitman, and M. Yor, “On Walsh’s Brownian motions,” inSeminaire deProbabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 275–293. Springer, 1989. Math.Review.

[10] M. Barlow, J. Pitman, and M. Yor, “Une extension multidimensionnelle de la loi de l’arcsinus,” inSeminaire de Probabilites XXIII, vol. 1372 ofLecture Notes in Math.,pp. 294–314. Springer, 1989. Math. Review.

[11] S. Kozlov, J. Pitman, and M. Yor, “Brownian interpretations of an elliptic integral,” inSeminar on Stochastic Processes, 1991, pp. 83–95. Birkhauser, Boston, 1992. Math.Review.

[12] S. Kozlov, J. Pitman, and M. Yor, “Wiener football,”Theory Prob. Appl.37 (1992) 550–553.

[13] S. Asmussen, P. Glynn, and J. Pitman, “Discretization error in simulation ofone-dimensional reflecting Brownian motion,”Ann. Applied Prob.5 (1995) 875–896, Math.Review.

[14] J. Pitman, “Cyclically stationary Brownian local time processes,”Probab. Th. Rel. Fields106(1996) 299–329, Article [.ps.Z], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math.Review.

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[15] J. Pitman, “Partition structures derived from Brownian motion and stable subordinators,”Bernoulli3 (1997) 79–96, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[16] M. Jeanblanc, J. Pitman, and M. Yor, “The Feynman-Kac formula and decomposition ofBrownian paths,”Comput. Appl. Math.16 (1997) 27–52, Abstract[.txt], Preprint [.ps.Z],Math. Review.

[17] J. Pitman and M. Yor, “Random Brownian scaling identities and splicing of Besselprocesses,”Ann. Probab.26 (1998) 1683–1702, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

[18] J. Pitman, “Brownian motion, bridge, excursion and meander characterized by sampling atindependent uniform times,”Electron. J. Probab.4 (1999) Paper 11, 1–33, Article, Math.Review.

[19] R. Pemantle, Y. Peres, J. Pitman, and M. Yor, “Where did the Brownian particle go?,”Electron. J. Probab.6 (2001) Paper 10, 1–22, Article, Math. Review.

Brownian trees

[1] J. Neveu and J. Pitman, “Renewal Property of the Extrema and Tree Property of aOne-dimensional Brownian Motion,” inSeminaire de Probabilites XXIII, vol. 1372 ofLectureNotes in Math., pp. 239–247. Springer, 1989. Math. Review.

[2] J. Neveu and J. Pitman, “The Branching Process in a Brownian Excursion,” inSeminaire deProbabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 248–257. Springer, 1989. Math.Review.

Brownian variations

[1] M. E. H. Ismail and J. Pitman, “Algebraic evaluations of some Euler integrals, duplicationformulae for Appell’s hypergeometric functionF1, and Brownian variations,”Canad. J.Math.52 (2000) 961–981, Abstract[.txt], Preprint [.ps.Z], Math. Review.

12

Card shuffling

[1] P. Diaconis, J. Fill, and J. Pitman, “Analysis of top in at random shuffles,”Combinatorics,Probability and Computing1 (1992) 135–155, Math. Review.

[2] P. Diaconis, M. McGrath, and J. Pitman, “Riffle shuffles, cycles and descents,”Combinatorica15 (1995) 11–29, Math. Review.

Cauchy process

[1] J. Pitman and M. Yor, “Level crossings of a Cauchy process,”Annals of Probability14 (1986)780–792.

Characteristic functions

[1] C. Heathcote and J. Pitman, “An inequality for characteristic functions,”Bull. Aust. Math.Soc.6 (1972) 1–10, Math. Review.

Coagulation

[1] R. Sheth and J. Pitman, “Coagulation and branching process models of gravitationalclustering,”Mon. Not. R. Astron. Soc.289(1997) 66–80, Preprint [.ps.Z].

Coalescents

[1] S. Evans and J. Pitman, “Construction of Markovian coalescents,”Ann. Inst. Henri Poincare34 (1998) 339–383, Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math.Review.

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[2] J. Pitman, “Coalescent random forests,”J. Comb. Theory A.85 (1999) 165–193, Article[.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] J. Pitman, “Coalescents with multiple collisions,”Ann. Probab.27 (1999) 1870–1902, Article[.pdf], Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[4] J. Bertoin and J. Pitman, “Two coalescents derived from the ranges of stable subordinators,”Electron. J. Probab.5 (2000) no. 7, 17 pp., Article, Math. Review.

[5] J. Pitman, “Combinatorial Stochastic Processes,” Tech. Rep. 621, Dept. Statistics, U.C.Berkeley, 2002. Lecture notes for St. Flour course, July 2002. Corrections to version of July1,2002, Abstract[.txt], Preprint [.ps.Z].

Combinatorial asymptotics

[1] J. Bennies and J. Pitman, “Asymptotics of the Hurwitz binomial distribution related to mixedPoisson Galton-Watson trees,”Combinatorics, Probability and Computing10 (2001)203–211, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Combinatorial stochastic processes

[1] D. Aldous and J. Pitman, “Two recursive decompositions of Brownian bridge related to theasymptotics of random mappings,” Tech. Rep. 595, Dept. Statistics, U.C. Berkeley, 2002.Abstract[.txt], Preprint [.ps.Z].

[2] D. Aldous and J. Pitman, “The asymptotic distribution of the diameter of a random mapping,”C.R. Acad. Sci. Paris, Ser. I334(2002) 1021–1024, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] D. Aldous, G. Miermont, and J. Pitman, “Brownian bridge asymptotics for randomp-mappings,” Tech. Rep. 624, Dept. Statistics, U.C. Berkeley, 2002. Abstract[.txt], Preprint[.ps.Z].

[4] J. Pitman, “Combinatorial Stochastic Processes,” Tech. Rep. 621, Dept. Statistics, U.C.Berkeley, 2002. Lecture notes for St. Flour course, July 2002. Corrections to version of July1,2002, Abstract[.txt], Preprint [.ps.Z].

14

Conditional independence

[1] J. Pitman and T. Speed, “A note on random times,”Stoch. Proc. Appl.1 (1973) 369–374,Math. Review.

[2] M. Jacobsen and J. Pitman, “Birth, death and conditioning of Markov chains,”Annals ofProbability5 (1977) 430–450, Math. Review.

Conditioned processes

[1] J. Pitman, “Path decomposition for conditional Brownian motion,” Tech. Rep. 11, Inst. Math.Stat., Univ. of Copenhagen, 1974.

[2] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[3] M. Jacobsen and J. Pitman, “Birth, death and conditioning of Markov chains,”Annals ofProbability5 (1977) 430–450, Math. Review.

[4] M. Klass and J. Pitman, “Limit laws for Brownian motion conditioned to reach a high level,”Statistics and Probability Letters17 (1993) 13–17, Math. Review.

Continuum random trees

[1] D. Aldous and J. Pitman, “Inhomogeneous continuum random trees and the entranceboundary of the additive coalescent,”Probab. Th. Rel. Fields118(2000) 455–482, Article[.pdf], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Convex minorant

[1] J. Pitman, “Remarks on the convex minorant of Brownian motion,” inSeminar on StochasticProcesses, 1982, pp. 219–227. Birkhauser, Boston, 1983. Math. Review.

15

Coupling

[1] J. Pitman, “Uniform rates of convergence for Markov chain transition probabilities,”Z.Wahrsch. Verw. Gebiete29 (1974) 193–227, Math. Review.

[2] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

[3] J. Pitman, “On coupling of Markov chains,”Z. Wahrsch. Verw. Gebiete35 (1976) 315–322,Math. Review.

[4] D. Aldous and J. Pitman, “On the zero-one law for exchangeable events,”Annals ofProbability7 (1979) 704–723, Math. Review.

Crossings

[1] K. Burdzy, J. Pitman, and M. Yor, “Some Asymptotic Laws for Crossings and Excursions,” inColloque Paul Levy sur les Processus Stochastiques, Asterisque 157-158, pp. 59–74. SocieteMathematique de France, 1988. Math. Review.

[2] K. Burdzy, J. Pitman, and M. Yor, “Brownian crossings between spheres,”J. of MathematicalAnalysis and Applications148, No. 1(1990) 101–120, Math. Review.

Cycles

[1] P. Diaconis, M. McGrath, and J. Pitman, “Riffle shuffles, cycles and descents,”Combinatorica15 (1995) 11–29, Math. Review.

Cyclically stationary processes

[1] J. Pitman, “Cyclically stationary Brownian local time processes,”Probab. Th. Rel. Fields106(1996) 299–329, Article [.ps.Z], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math. Review.

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[2] S. Evans and J. Pitman, “Stopped Markov chains with stationary occupation times,”Probab.Th. Rel. Fields109(1997) 425–433, Abstract[.txt], Preprint [.ps.Z], Math. Review.

David Blackwell

[1] J. Pitman, “Some developments of the Blackwell-MacQueen urn scheme,” inStatistics,Probability and Game Theory; Papers in honor of David Blackwell, T. F. et al., ed., vol. 30 ofLecture Notes-Monograph Series, pp. 245–267. Institute of Mathematical Statistics,Hayward, California, 1996. Preprint [.ps.Z], Math. Review.

Death times

[1] M. Jacobsen and J. Pitman, “Birth, death and conditioning of Markov chains,”Annals ofProbability5 (1977) 430–450, Math. Review.

Decomposition at the maximum

[1] P. Greenwood and J. Pitman, “Fluctuation identities for Levy processes and splitting at themaximum,”Advances in Applied Probability12 (1980) 893–902, Math. Review.

[2] P. Greenwood and J. Pitman, “Fluctuation identities for random walk by path decompositionat the maximum,”Advances in Applied Probability12 (1980) 291–293.

[3] J. Pitman and M. Yor, “Decomposition at the maximum for excursions and bridges ofone-dimensional diffusions,” inIto’s Stochastic Calculus and Probability Theory, N. Ikeda,S. Watanabe, M. Fukushima, and H. Kunita, eds., pp. 293–310. Springer-Verlag, 1996. Math.Review.

17

Descents

[1] P. Diaconis, M. McGrath, and J. Pitman, “Riffle shuffles, cycles and descents,”Combinatorica15 (1995) 11–29, Math. Review.

Discretization error

[1] S. Asmussen, P. Glynn, and J. Pitman, “Discretization error in simulation of one-dimensionalreflecting Brownian motion,”Ann. Applied Prob.5 (1995) 875–896, Math. Review.

Divergence

[1] L. Dubins and J. Pitman, “A divergent, two-parameter, bounded martingale,”Proc. Amer.Math. Soc.78 (1980), no. 3, 414–416, Math. Review.

Divergent integrals

[1] J. Pitman and M. Yor, “Some divergent integrals of Brownian motion,” inAnalytic andGeometric Stochastics: Papers in Honour of G. E. H. Reuter (Special supplement to Adv.App. Prob), D. G. Kendall, J. F. C. Kingman, and D. Williams, eds., pp. 109–116. AppliedProb. Trust, 1986. Math. Review.

Duality

[1] H. Dette, J. Fill, J. Pitman, and W. Studden, “Wall and Siegmund duality relations for birthand death chains with reflecting barrier,”Journal of Theoretical Probability10 (1997)349–374, Preprint [.ps.Z], Math. Review.

18

Elliptic integral

[1] S. Kozlov, J. Pitman, and M. Yor, “Brownian interpretations of an elliptic integral,” inSeminar on Stochastic Processes, 1991, pp. 83–95. Birkhauser, Boston, 1992. Math. Review.

[2] S. Kozlov, J. Pitman, and M. Yor, “Wiener football,”Theory Prob. Appl.37 (1992) 550–553.

Empirical distributions

[1] J. Pitman and R. Stanley, “A polytope related to empirical distributions, plane trees, parkingfunctions and the associahedron,”Discrete and Computational Geometry27 (2002) 603–634,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Entrance boundaries

[1] D. Aldous and J. Pitman, “Inhomogeneous continuum random trees and the entranceboundary of the additive coalescent,”Probab. Th. Rel. Fields118(2000) 455–482, Article[.pdf], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Enumerations

[1] J. Pitman, “Enumerations of trees and forests related to branching processes and randomwalks,” in Microsurveys in Discrete Probability, D. Aldous and J. Propp, eds., no. 41 inDIMACS Ser. Discrete Math. Theoret. Comp. Sci, pp. 163–180. Amer. Math. Soc.,Providence RI, 1998. Abstract[.txt], Preprint [.ps.Z], Math. Review.

19

Ergodic theory

[1] L. Dubins and J. Pitman, “A pointwise ergodic theorem for the group of rational rotations,”Trans. Amer. Math. Soc.251(1980) 299–308, Math. Review.

[2] J. Pitman and M. Yor, “Some properties of the arc sine law related to its invariance under afamily of rational maps,” Tech. Rep. 558, Dept. Statistics, U.C. Berkeley, 1999.Abstract[.txt], Preprint [.ps.Z].

Euler integrals

[1] M. E. H. Ismail and J. Pitman, “Algebraic evaluations of some Euler integrals, duplicationformulae for Appell’s hypergeometric functionF1, and Brownian variations,”Canad. J.Math.52 (2000) 961–981, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Ewens sampling formula

[1] J. Pitman, “The two-parameter generalization of Ewens’ random partition structure,” Tech.Rep. 345, Dept. Statistics, U.C. Berkeley, 1992.

Exchangeability

[1] B. Hansen and J. Pitman, “Prediction rules and exchangeable sequences related to speciessampling,”Stat. and Prob. Letters46 (2000) 251–256, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

20

Exchangeable events

[1] D. Aldous and J. Pitman, “On the zero-one law for exchangeable events,”Annals ofProbability7 (1979) 704–723, Math. Review.

Exchangeable random partitions

[1] J. Pitman, “Exchangeable and partially exchangeable random partitions,”Probab. Th. Rel.Fields102(1995) 145–158, Math. Review.

Excursions

[1] J. Pitman, “Levy systems and path decompositions,” inSeminar on Stochastic Processes,1981, pp. 79–110. Birkhauser, Boston, 1981. Math. Review.

[2] J. Pitman and M. Yor, “A decomposition of Bessel bridges,”Z. Wahrsch. Verw. Gebiete59(1982) 425–457, Math. Review.

[3] J. Pitman, “Stationary excursions,” inSeminaire de Probabilites XXI, vol. 1247 ofLectureNotes in Math., pp. 289–302. Springer, 1986. Math. Review.

[4] K. Burdzy, J. Pitman, and M. Yor, “Some Asymptotic Laws for Crossings and Excursions,”in Colloque Paul Levy sur les Processus Stochastiques, Asterisque 157-158, pp. 59–74.Societe Mathematique de France, 1988. Math. Review.

[5] M. Perman, J. Pitman, and M. Yor, “Size-biased Sampling of Poisson Point Processes andExcursions,”Probab. Th. Rel. Fields92 (1992) 21–39, Math. Review.

[6] J. Pitman and M. Yor, “Decomposition at the maximum for excursions and bridges ofone-dimensional diffusions,” inIto’s Stochastic Calculus and Probability Theory, N. Ikeda,S. Watanabe, M. Fukushima, and H. Kunita, eds., pp. 293–310. Springer-Verlag, 1996.Math. Review.

[7] J. Pitman and M. Yor, “On the lengths of excursions of some Markov processes,” inSeminaire de Probabilites XXXI, vol. 1655 ofLecture Notes in Math., pp. 272–286.Springer, 1997. Abstract[.txt], Preprint [.ps.Z], Math. Review.

21

[8] J. Pitman and M. Yor, “On the relative lengths of excursions derived from a stablesubordinator,” inSeminaire de Probabilites XXXI, vol. 1655 ofLecture Notes in Math.,pp. 287–305. Springer, 1997. Abstract[.txt], Preprint [.ps.Z], Math. Review.

[9] J. Pitman and M. Yor, “Laplace transforms related to excursions of a one-dimensionaldiffusion,” Bernoulli5 (1999) 249–255, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[10] J. Pitman and M. Yor, “Hitting, occupation, and inverse local times of one-dimensionaldiffusions: martingale and excursion approaches,”Bernoulli9 (2003) 1–24, Abstract[.txt],Preprint [.ps.Z].

Feynman-Kac formula

[1] M. Jeanblanc, J. Pitman, and M. Yor, “The Feynman-Kac formula and decomposition ofBrownian paths,”Comput. Appl. Math.16 (1997) 27–52, Abstract[.txt], Preprint [.ps.Z],Math. Review.

[2] P. J. Fitzsimmons and J. Pitman, “Kac’s moment formula and the Feynman-Kac formula foradditive functionals of a Markov process,”Stochastic Process. Appl.79 (1999) 117–134,Preprint [.ps.Z], Article [.pdf], ScienceDirect, Math. Review.

Fluctuation theory

[1] P. Greenwood and J. Pitman, “Fluctuation identities for Levy processes and splitting at themaximum,”Advances in Applied Probability12 (1980) 893–902, Math. Review.

[2] P. Greenwood and J. Pitman, “Fluctuation identities for random walk by path decompositionat the maximum,”Advances in Applied Probability12 (1980) 291–293.

Forest volume decompositions

[1] J. Pitman, “Forest volume decompositions and Abel-Cayley-Hurwitz multinomialexpansions,”J. Comb. Theory A.98 (2002) 175–191, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

22

Fragmentation processes

[1] J. Pitman, “Combinatorial Stochastic Processes,” Tech. Rep. 621, Dept. Statistics, U.C.Berkeley, 2002. Lecture notes for St. Flour course, July 2002. Corrections to version of July1,2002, Abstract[.txt], Preprint [.ps.Z].

GEM distribution

[1] J. Pitman, “Poisson-Dirichlet and GEM invariant distributions for split-and-mergetransformations of an interval partition,”Combinatorics, Probability and Computing11(2002) 501–514, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Girsanov transforms

[1] J. Pitman and M. Yor, “Sur une decomposition des ponts de Bessel,” inFunctional Analysis inMarkov Processes, M. Fukushima, ed., vol. 923 ofLecture Notes in Math, pp. 276–285.Springer, 1982. Math. Review.

Gravitational clustering

[1] R. Sheth and J. Pitman, “Coagulation and branching process models of gravitationalclustering,”Mon. Not. R. Astron. Soc.289(1997) 66–80, Preprint [.ps.Z].

Hitting times

[1] J. Pitman and M. Yor, “Hitting, occupation, and inverse local times of one-dimensionaldiffusions: martingale and excursion approaches,”Bernoulli9 (2003) 1–24, Abstract[.txt],Preprint [.ps.Z].

23

Homogeneous functionals

[1] P. Carmona, F. Petit, J. Pitman, and M. Yor, “On the laws of homogeneous functionals of theBrownian bridge,”Studia Sci. Math. Hungar.35 (1999) 445–455, Abstract[.txt], Preprint[.ps.Z], Math. Review.

Hurwitz binomial distribution

[1] J. Bennies and J. Pitman, “Asymptotics of the Hurwitz binomial distribution related to mixedPoisson Galton-Watson trees,”Combinatorics, Probability and Computing10 (2001)203–211, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Hyperbolic functions

[1] J. Pitman and M. Yor, “Infinitely divisible laws associated with hyperbolic functions,” Tech.Rep. 581, Dept. Statistics, U.C. Berkeley, 2000. To appear inCanadian Journal ofMathematics, Abstract[.txt], Preprint [.ps.Z].

Identities

[1] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

[2] J. Pitman, “An identity for stopping times of a Markov Process,” inStudies in Probability andStatistics, pp. 41–57. Jerusalem Academic Press, 1974. Math. Review.

[3] J. Bertoin and J. Pitman, “Path Transformations Connecting Brownian Bridge, Excursion andMeander,”Bull. Sci. Math. (2)118(1994) 147–166, Math. Review.

[4] J. Pitman and M. Yor, “Quelques identites en loi pour les processus de Bessel,” inHommageaP.A. Meyer et J. Neveu, Asterisque, pp. 249–276. Soc. Math. de France, 1996. Math. Review.

24

Identities in law

[1] J. Bertoin and J. Pitman, “Path Transformations Connecting Brownian Bridge, Excursion andMeander,”Bull. Sci. Math. (2)118(1994) 147–166, Math. Review.

[2] J. Pitman and M. Yor, “Quelques identites en loi pour les processus de Bessel,” inHommageaP.A. Meyer et J. Neveu, Asterisque, pp. 249–276. Soc. Math. de France, 1996. Math. Review.

Inequalities

[1] C. Heathcote and J. Pitman, “An inequality for characteristic functions,”Bull. Aust. Math.Soc.6 (1972) 1–10, Math. Review.

[2] J. Pitman, “A note onL2 maximal inequalities,” inSeminaire de Probabilites XV, vol. 850 ofLecture Notes in Math, pp. 251–258. Springer, 1981. Math. Review.

Infinitely divisible laws

[1] J. Pitman and M. Yor, “Bessel processes and infinitely divisible laws,” inStochastic Integrals,vol. 851 ofLecture Notes in Math., pp. 285–370. Springer, 1981. Math. Review.

[2] J. Pitman and M. Yor, “Infinitely divisible laws associated with hyperbolic functions,” Tech.Rep. 581, Dept. Statistics, U.C. Berkeley, 2000. To appear inCanadian Journal ofMathematics, Abstract[.txt], Preprint [.ps.Z].

Interval partitions

[1] J. Pitman and M. Yor, “Arcsine laws and interval partitions derived from a stablesubordinator,”Proc. London Math. Soc. (3)65 (1992) 326–356, Math. Review.

[2] J. Pitman, “Poisson-Dirichlet and GEM invariant distributions for split-and-mergetransformations of an interval partition,”Combinatorics, Probability and Computing11(2002) 501–514, Abstract[.txt], Preprint [.ps.Z], Math. Review.

25

Invariance principles

[1] D. Aldous and J. Pitman, “Invariance principles for non-uniform random mappings andtrees,” inAsymptotic Combinatorics with Aplications in Mathematical Physics, V. Malyshevand A. M. Vershik, eds., pp. 113–147. Kluwer Academic Publishers, 2002. Abstract[.txt],Preprint [.ps.Z].

Jacobi theta functions

[1] P. Biane, J. Pitman, and M. Yor, “Probability laws related to the Jacobi theta and Riemannzeta functions, and Brownian excursions,”Bull. Amer. Math. Soc.38 (2001) 435–465, Article,Math. Review.

Jim MacQueen

[1] J. Pitman, “Some developments of the Blackwell-MacQueen urn scheme,” inStatistics,Probability and Game Theory; Papers in honor of David Blackwell, T. F. et al., ed., vol. 30 ofLecture Notes-Monograph Series, pp. 245–267. Institute of Mathematical Statistics,Hayward, California, 1996. Preprint [.ps.Z], Math. Review.

Kacs moment formula

[1] P. J. Fitzsimmons and J. Pitman, “Kac’s moment formula and the Feynman-Kac formula foradditive functionals of a Markov process,”Stochastic Process. Appl.79 (1999) 117–134,Preprint [.ps.Z], Article [.pdf], ScienceDirect, Math. Review.

26

Knights identity

[1] J. Pitman and M. Yor, “Dilatations d’espace-temps, rearrangements des trajectoiresbrowniennes, et quelques extensions d’une identite de Knight,”C.R. Acad. Sci. Parist. 316,Serie I (1993) 723–726, Math. Review.

Laplace transforms

[1] J. Pitman and M. Yor, “Laplace transforms related to excursions of a one-dimensionaldiffusion,” Bernoulli5 (1999) 249–255, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Lattice paths

[1] J. Pitman, “A lattice path model for the Bessel polynomials,” Tech. Rep. 551, Dept. Statistics,U.C. Berkeley, 1999. Abstract[.txt], Preprint [.ps.Z].

Level crossings

[1] J. Pitman and M. Yor, “Level crossings of a Cauchy process,”Annals of Probability14 (1986)780–792.

Levy Khintchine representations

[1] J. Pitman and M. Yor, “A decomposition of Bessel bridges,”Z. Wahrsch. Verw. Gebiete59(1982) 425–457, Math. Review.

27

Levy processes

[1] P. Greenwood and J. Pitman, “Fluctuation identities for Levy processes and splitting at themaximum,”Advances in Applied Probability12 (1980) 893–902, Math. Review.

[2] J. Pitman and M. Yor, “Infinitely divisible laws associated with hyperbolic functions,” Tech.Rep. 581, Dept. Statistics, U.C. Berkeley, 2000. To appear inCanadian Journal ofMathematics, Abstract[.txt], Preprint [.ps.Z].

[3] M. Jeanblanc, J. Pitman, and M. Yor, “Self-similar processes with independent incrementsassociated with Levy and Bessel processes,”Stochastic Processes Appl.100(2002) 223–232,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Levy systems

[1] J. Pitman, “Levy systems and path decompositions,” inSeminar on Stochastic Processes,1981, pp. 79–110. Birkhauser, Boston, 1981. Math. Review.

[2] S. Evans and J. Pitman, “Construction of Markovian coalescents,”Ann. Inst. Henri Poincare34 (1998) 339–383, Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math.Review.

Local time

[1] P. Greenwood and J. Pitman, “Construction of local time and Poisson point processes fromnested arrays,”Journal of the London Mathematical Society22 (1980) 182–192, Math.Review.

[2] J. Pitman and M. Yor, “A decomposition of Bessel bridges,”Z. Wahrsch. Verw. Gebiete59(1982) 425–457, Math. Review.

[3] J. Pitman, “Cyclically stationary Brownian local time processes,”Probab. Th. Rel. Fields106(1996) 299–329, Article [.ps.Z], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[4] J. Pitman, “The SDE solved by local times of a Brownian excursion or bridge derived fromthe height profile of a random tree or forest,”Ann. Probab.27 (1999) 261–283, Article [.pdf],Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

28

[5] J. Pitman, “The distribution of local times of Brownian bridge,” inSeminaire de ProbabilitesXXXIII, vol. 1709 ofLecture Notes in Math., pp. 388–394. Springer, 1999. Abstract[.txt],Preprint [.ps.Z], Math. Review.

[6] J. Pitman and M. Yor, “Hitting, occupation, and inverse local times of one-dimensionaldiffusions: martingale and excursion approaches,”Bernoulli9 (2003) 1–24, Abstract[.txt],Preprint [.ps.Z].

Local times

[1] P. Greenwood and J. Pitman, “Construction of local time and Poisson point processes fromnested arrays,”Journal of the London Mathematical Society22 (1980) 182–192, Math.Review.

[2] J. Pitman and M. Yor, “A decomposition of Bessel bridges,”Z. Wahrsch. Verw. Gebiete59(1982) 425–457, Math. Review.

[3] J. Pitman, “Cyclically stationary Brownian local time processes,”Probab. Th. Rel. Fields106(1996) 299–329, Article [.ps.Z], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[4] J. Pitman, “The SDE solved by local times of a Brownian excursion or bridge derived fromthe height profile of a random tree or forest,”Ann. Probab.27 (1999) 261–283, Article [.pdf],Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[5] J. Pitman, “The distribution of local times of Brownian bridge,” inSeminaire de ProbabilitesXXXIII, vol. 1709 ofLecture Notes in Math., pp. 388–394. Springer, 1999. Abstract[.txt],Preprint [.ps.Z], Math. Review.

[6] J. Pitman and M. Yor, “Hitting, occupation, and inverse local times of one-dimensionaldiffusions: martingale and excursion approaches,”Bernoulli9 (2003) 1–24, Abstract[.txt],Preprint [.ps.Z].

Locally uniform measure

[1] D. Freedman and J. Pitman, “A singular measure which is locally uniform,”Proc. Amer.Math. Soc.108(1990) 371–381, Math. Review.

29

Markov chains

[1] J. Pitman, “Uniform rates of convergence for Markov chain transition probabilities,”Z.Wahrsch. Verw. Gebiete29 (1974) 193–227, Math. Review.

[2] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

[3] J. Pitman, “An identity for stopping times of a Markov Process,” inStudies in Probability andStatistics, pp. 41–57. Jerusalem Academic Press, 1974. Math. Review.

[4] J. Pitman, “On coupling of Markov chains,”Z. Wahrsch. Verw. Gebiete35 (1976) 315–322,Math. Review.

[5] J. Pitman, “Occupation measures for Markov chains,”Advances in Applied Probability9(1977) 69–86.

[6] M. Jacobsen and J. Pitman, “Birth, death and conditioning of Markov chains,”Annals ofProbability5 (1977) 430–450, Math. Review.

[7] D. Aldous and J. Pitman, “On the zero-one law for exchangeable events,”Annals ofProbability7 (1979) 704–723, Math. Review.

[8] S. Evans and J. Pitman, “Stopped Markov chains with stationary occupation times,”Probab.Th. Rel. Fields109(1997) 425–433, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[9] D. Aldous and J. Pitman, “Tree-valued Markov chains derived from Galton-Watsonprocesses,”Ann. Inst. Henri Poincare34 (1998) 637–686, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Markov functions

[1] L. C. G. Rogers and J. Pitman, “Markov functions,”Annals of Probability9 (1981) 573–582,Math. Review.

30

Markov processes

[1] J. Pitman, “Levy systems and path decompositions,” inSeminar on Stochastic Processes,1981, pp. 79–110. Birkhauser, Boston, 1981. Math. Review.

[2] J. Pitman and M. Yor, “On the lengths of excursions of some Markov processes,” inSeminaire de Probabilites XXXI, vol. 1655 ofLecture Notes in Math., pp. 272–286. Springer,1997. Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] S. Evans and J. Pitman, “Construction of Markovian coalescents,”Ann. Inst. Henri Poincare34 (1998) 339–383, Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math.Review.

[4] S. Evans and J. Pitman, “Stationary Markov processes related to stable Ornstein-Uhlenbeckprocesses and the additive coalescent,”Stochastic Processes Appl.77 (1998) 175–185,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[5] P. J. Fitzsimmons and J. Pitman, “Kac’s moment formula and the Feynman-Kac formula foradditive functionals of a Markov process,”Stochastic Process. Appl.79 (1999) 117–134,Preprint [.ps.Z], Article [.pdf], ScienceDirect, Math. Review.

Markovian bridges

[1] P. Fitzsimmons, J. Pitman, and M. Yor, “Markovian bridges: construction, Palminterpretation, and splicing,” inSeminar on Stochastic Processes, 1992, E. Cinlar, K. Chung,and M. Sharpe, eds., pp. 101–134. Birkhauser, Boston, 1993. Math. Review.

Martingales

[1] L. Dubins and J. Pitman, “A divergent, two-parameter, bounded martingale,”Proc. Amer.Math. Soc.78 (1980), no. 3, 414–416, Math. Review.

[2] J. Pitman, “A note onL2 maximal inequalities,” inSeminaire de Probabilites XV, vol. 850 ofLecture Notes in Math, pp. 251–258. Springer, 1981. Math. Review.

31

[3] J. Pitman and M. Yor, “Hitting, occupation, and inverse local times of one-dimensionaldiffusions: martingale and excursion approaches,”Bernoulli9 (2003) 1–24, Abstract[.txt],Preprint [.ps.Z].

Maximal inequality

[1] L. Dubins and J. Pitman, “A maximal inequality for skew fields,”Z. Wahrsch. Verw. Gebiete52 (1980) 219–227, Math. Review.

Maximum and minimum

[1] J. Pitman and M. Yor, “The law of the maximum of a Bessel bridge,”Electron. J. Probab.4(1999) Paper 15, 1–35, Article, Math. Review.

[2] J. Pitman and M. Yor, “Path decompositions of a Brownian bridge related to the ratio of itsmaximum and amplitude,”Studia Sci. Math. Hungar.35 (1999), no. 520, 457–474,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] J. Bertoin, J. Pitman, and J. R. de Chavez, “Constructions of a Brownian path with a givenminimum,” Electronic Comm. Probab.4 (1999) Paper 5, 1–7, Article, Math. Review.

Measurable functions

[1] S. Evans and J. Pitman, “Does every Borel function have a somewhere continuousmodification?,”Real Analysis Exchange18(1)(1993) 276–280, Math. Review.

Multivariate disributions

[1] M. Barlow, J. Pitman, and M. Yor, “Une extension multidimensionnelle de la loi de l’arcsinus,” inSeminaire de Probabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 294–314.Springer, 1989. Math. Review.

32

Nested arrays

[1] P. Greenwood and J. Pitman, “Construction of local time and Poisson point processes fromnested arrays,”Journal of the London Mathematical Society22 (1980) 182–192, Math.Review.

Occupation measures

[1] J. Pitman, “Occupation measures for Markov chains,”Advances in Applied Probability9(1977) 69–86.

[2] R. Pemantle, Y. Peres, J. Pitman, and M. Yor, “Where did the Brownian particle go?,”Electron. J. Probab.6 (2001) Paper 10, 1–22, Article, Math. Review.

Occupation times

[1] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

[2] J. Pitman, “An identity for stopping times of a Markov Process,” inStudies in Probability andStatistics, pp. 41–57. Jerusalem Academic Press, 1974. Math. Review.

[3] J. Pitman and M. Yor, “A decomposition of Bessel bridges,”Z. Wahrsch. Verw. Gebiete59(1982) 425–457, Math. Review.

[4] S. Evans and J. Pitman, “Stopped Markov chains with stationary occupation times,”Probab.Th. Rel. Fields109(1997) 425–433, Abstract[.txt], Preprint [.ps.Z], Math. Review.

One-dimensional diffusions

[1] J. Pitman and M. Yor, “Decomposition at the maximum for excursions and bridges ofone-dimensional diffusions,” inIto’s Stochastic Calculus and Probability Theory, N. Ikeda,

33

S. Watanabe, M. Fukushima, and H. Kunita, eds., pp. 293–310. Springer-Verlag, 1996. Math.Review.

[2] J. Pitman and M. Yor, “Laplace transforms related to excursions of a one-dimensionaldiffusion,” Bernoulli5 (1999) 249–255, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] J. Pitman and M. Yor, “Hitting, occupation, and inverse local times of one-dimensionaldiffusions: martingale and excursion approaches,”Bernoulli9 (2003) 1–24, Abstract[.txt],Preprint [.ps.Z].

Palm measures

[1] J. Pitman, “Stationary excursions,” inSeminaire de Probabilites XXI, vol. 1247 ofLectureNotes in Math., pp. 289–302. Springer, 1986. Math. Review.

[2] J. Pitman and M. Yor, “Arcsine laws and interval partitions derived from a stablesubordinator,”Proc. London Math. Soc. (3)65 (1992) 326–356, Math. Review.

[3] P. Fitzsimmons, J. Pitman, and M. Yor, “Markovian bridges: construction, Palminterpretation, and splicing,” inSeminar on Stochastic Processes, 1992, E. Cinlar, K. Chung,and M. Sharpe, eds., pp. 101–134. Birkhauser, Boston, 1993. Math. Review.

Parking functions

[1] J. Pitman and R. Stanley, “A polytope related to empirical distributions, plane trees, parkingfunctions and the associahedron,”Discrete and Computational Geometry27 (2002) 603–634,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Partially exchangeable random partitions

[1] J. Pitman, “Exchangeable and partially exchangeable random partitions,”Probab. Th. Rel.Fields102(1995) 145–158, Math. Review.

34

Particle systems

[1] D. Aldous and J. Pitman, “The asymptotic speed and shape of a particle system,” inProbability, Statistics and Analysis, London Math. Soc. Lecture Notes, pp. 1–23. CambridgeUniv. Press, 1983. Math. Review.

Partition structures

[1] J. Pitman, “The two-parameter generalization of Ewens’ random partition structure,” Tech.Rep. 345, Dept. Statistics, U.C. Berkeley, 1992.

[2] J. Pitman, “Exchangeable and partially exchangeable random partitions,”Probab. Th. Rel.Fields102(1995) 145–158, Math. Review.

[3] J. Pitman, “Partition structures derived from Brownian motion and stable subordinators,”Bernoulli3 (1997) 79–96, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[4] J. Pitman, “Combinatorial Stochastic Processes,” Tech. Rep. 621, Dept. Statistics, U.C.Berkeley, 2002. Lecture notes for St. Flour course, July 2002. Corrections to version of July1,2002, Abstract[.txt], Preprint [.ps.Z].

[5] J. Pitman, “Poisson-Kingman partitions,” inScience and Statistics: A Festschrift for TerrySpeed, D. R. Goldstein, ed., vol. 30 ofLecture Notes-Monograph Series, pp. 1–34. Institute ofMathematical Statistics, Hayward, California, 2003. Article, Abstract[.txt], Preprint [.ps.Z].

Path decomposition

[1] J. Pitman, “Path decomposition for conditional Brownian motion,” Tech. Rep. 11, Inst.Math. Stat., Univ. of Copenhagen, 1974.

[2] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[3] M. Jacobsen and J. Pitman, “Birth, death and conditioning of Markov chains,”Annals ofProbability5 (1977) 430–450, Math. Review.

35

[4] P. Greenwood and J. Pitman, “Fluctuation identities for Levy processes and splitting at themaximum,”Advances in Applied Probability12 (1980) 893–902, Math. Review.

[5] P. Greenwood and J. Pitman, “Fluctuation identities for random walk by path decompositionat the maximum,”Advances in Applied Probability12 (1980) 291–293.

[6] J. Pitman, “Levy systems and path decompositions,” inSeminar on Stochastic Processes,1981, pp. 79–110. Birkhauser, Boston, 1981. Math. Review.

[7] M. Klass and J. Pitman, “Limit laws for Brownian motion conditioned to reach a high level,”Statistics and Probability Letters17 (1993) 13–17, Math. Review.

[8] J. Pitman and M. Yor, “Decomposition at the maximum for excursions and bridges ofone-dimensional diffusions,” inIto’s Stochastic Calculus and Probability Theory, N. Ikeda,S. Watanabe, M. Fukushima, and H. Kunita, eds., pp. 293–310. Springer-Verlag, 1996.Math. Review.

[9] M. Jeanblanc, J. Pitman, and M. Yor, “The Feynman-Kac formula and decomposition ofBrownian paths,”Comput. Appl. Math.16 (1997) 27–52, Abstract[.txt], Preprint [.ps.Z],Math. Review.

[10] J. Pitman and M. Yor, “Path decompositions of a Brownian bridge related to the ratio of itsmaximum and amplitude,”Studia Sci. Math. Hungar.35 (1999), no. 520, 457–474,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[11] J. Bertoin, J. Pitman, and J. R. de Chavez, “Constructions of a Brownian path with a givenminimum,” Electronic Comm. Probab.4 (1999) Paper 5, 1–7, Article, Math. Review.

[12] D. Aldous and J. Pitman, “Two recursive decompositions of Brownian bridge related to theasymptotics of random mappings,” Tech. Rep. 595, Dept. Statistics, U.C. Berkeley, 2002.Abstract[.txt], Preprint [.ps.Z].

Path decompositions

[1] J. Pitman, “Path decomposition for conditional Brownian motion,” Tech. Rep. 11, Inst.Math. Stat., Univ. of Copenhagen, 1974.

[2] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[3] M. Jacobsen and J. Pitman, “Birth, death and conditioning of Markov chains,”Annals ofProbability5 (1977) 430–450, Math. Review.

36

[4] P. Greenwood and J. Pitman, “Fluctuation identities for Levy processes and splitting at themaximum,”Advances in Applied Probability12 (1980) 893–902, Math. Review.

[5] P. Greenwood and J. Pitman, “Fluctuation identities for random walk by path decompositionat the maximum,”Advances in Applied Probability12 (1980) 291–293.

[6] J. Pitman, “Levy systems and path decompositions,” inSeminar on Stochastic Processes,1981, pp. 79–110. Birkhauser, Boston, 1981. Math. Review.

[7] M. Klass and J. Pitman, “Limit laws for Brownian motion conditioned to reach a high level,”Statistics and Probability Letters17 (1993) 13–17, Math. Review.

[8] M. Jeanblanc, J. Pitman, and M. Yor, “The Feynman-Kac formula and decomposition ofBrownian paths,”Comput. Appl. Math.16 (1997) 27–52, Abstract[.txt], Preprint [.ps.Z],Math. Review.

[9] J. Pitman and M. Yor, “Path decompositions of a Brownian bridge related to the ratio of itsmaximum and amplitude,”Studia Sci. Math. Hungar.35 (1999), no. 520, 457–474,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[10] J. Bertoin, J. Pitman, and J. R. de Chavez, “Constructions of a Brownian path with a givenminimum,” Electronic Comm. Probab.4 (1999) Paper 5, 1–7, Article, Math. Review.

[11] D. Aldous and J. Pitman, “Two recursive decompositions of Brownian bridge related to theasymptotics of random mappings,” Tech. Rep. 595, Dept. Statistics, U.C. Berkeley, 2002.Abstract[.txt], Preprint [.ps.Z].

Path rearrangements

[1] J. Pitman and M. Yor, “Dilatations d’espace-temps, rearrangements des trajectoiresbrowniennes, et quelques extensions d’une identite de Knight,”C.R. Acad. Sci. Parist. 316,Serie I (1993) 723–726, Math. Review.

[2] D. Aldous and J. Pitman, “Two recursive decompositions of Brownian bridge related to theasymptotics of random mappings,” Tech. Rep. 595, Dept. Statistics, U.C. Berkeley, 2002.Abstract[.txt], Preprint [.ps.Z].

[3] D. Aldous and J. Pitman, “The asymptotic distribution of the diameter of a random mapping,”C.R. Acad. Sci. Paris, Ser. I334(2002) 1021–1024, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

37

Path splicing

[1] P. Fitzsimmons, J. Pitman, and M. Yor, “Markovian bridges: construction, Palminterpretation, and splicing,” inSeminar on Stochastic Processes, 1992, E. Cinlar, K. Chung,and M. Sharpe, eds., pp. 101–134. Birkhauser, Boston, 1993. Math. Review.

Path transformations

[1] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[2] J. Bertoin and J. Pitman, “Path Transformations Connecting Brownian Bridge, Excursion andMeander,”Bull. Sci. Math. (2)118(1994) 147–166, Math. Review.

Permutations

[1] P. Diaconis and J. Pitman, “Permutations, record values and random measures.” Unpublishedlecture notes. Dept. Statistics, U.C. Berkeley, 1986.

[2] P. Diaconis, J. Fill, and J. Pitman, “Analysis of top in at random shuffles,”Combinatorics,Probability and Computing1 (1992) 135–155, Math. Review.

[3] P. Diaconis, M. McGrath, and J. Pitman, “Riffle shuffles, cycles and descents,”Combinatorica15 (1995) 11–29, Math. Review.

Planar Brownian motion

[1] J. Pitman and M. Yor, “The asymptotic joint distribution of windings of planar Brownianmotion,” Bulletin of the American Mathematical Society10 (1984) 109–111, Math. Review.

[2] J. Pitman and M. Yor, “Asymptotic laws of planar Brownian motion,”Annals of Probability14 (1986) 733–779, Article [.pdf], Math. Review.

38

[3] J. Pitman and M. Yor, “Complementsa l’etude asymptotique des nombres de tours dumouvement brownien complexe autour d’un nombre fini de points,”C.R. Acad. Sc. Paris,Serie I 305(1987) 757–760, Math. Review.

[4] J. Pitman and M. Yor, “Further asymptotic laws of planar Brownian motion,”Annals ofProbability17 (1989) 965–1011, Article [.pdf], Math. Review.

Planar arcs

[1] A. Adhikari and J. Pitman, “The shortest planar arc of width one,”Amer. Math. Monthly96,No 4 (1989) 309–327, Article [.pdf], Math. Review.

Plane trees

[1] J. Pitman and R. Stanley, “A polytope related to empirical distributions, plane trees, parkingfunctions and the associahedron,”Discrete and Computational Geometry27 (2002) 603–634,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Point process

[1] J. Pitman, “Levy systems and path decompositions,” inSeminar on Stochastic Processes,1981, pp. 79–110. Birkhauser, Boston, 1981. Math. Review.

Poisson-Dirichlet distribution

[1] J. Pitman and M. Yor, “The two-parameter Poisson-Dirichlet distribution derived from astable subordinator,”Ann. Probab.25 (1997) 855–900, Article [.pdf], Project Euclid,Abstract[.txt], Preprint [.ps.Z], Math. Review.

39

[2] J. Pitman, “Poisson-Dirichlet and GEM invariant distributions for split-and-mergetransformations of an interval partition,”Combinatorics, Probability and Computing11(2002) 501–514, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Poisson point processes

[1] P. Greenwood and J. Pitman, “Construction of local time and Poisson point processes fromnested arrays,”Journal of the London Mathematical Society22 (1980) 182–192, Math.Review.

[2] M. Perman, J. Pitman, and M. Yor, “Size-biased Sampling of Poisson Point Processes andExcursions,”Probab. Th. Rel. Fields92 (1992) 21–39, Math. Review.

Polynomials with only real zeros

[1] J. Pitman, “Probabilistic bounds on the coefficients of polynomials with only real zeros,”J.Comb. Theory A.77 (1997) 279–303, Article [.pdf], ScienceDirect, Abstract[.txt], Preprint[.ps.Z], Math. Review.

Polytopes

[1] J. Pitman and R. Stanley, “A polytope related to empirical distributions, plane trees, parkingfunctions and the associahedron,”Discrete and Computational Geometry27 (2002) 603–634,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Prediction rules

[1] J. Pitman, “Some developments of the Blackwell-MacQueen urn scheme,” inStatistics,Probability and Game Theory; Papers in honor of David Blackwell, T. F. et al., ed., vol. 30 ofLecture Notes-Monograph Series, pp. 245–267. Institute of Mathematical Statistics,Hayward, California, 1996. Preprint [.ps.Z], Math. Review.

40

[2] B. Hansen and J. Pitman, “Prediction rules and exchangeable sequences related to speciessampling,”Stat. and Prob. Letters46 (2000) 251–256, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Probabilistic bounds

[1] J. Pitman, “Probabilistic bounds on the coefficients of polynomials with only real zeros,”J.Comb. Theory A.77 (1997) 279–303, Article [.pdf], ScienceDirect, Abstract[.txt], Preprint[.ps.Z], Math. Review.

Probabilistic combinatorics

[1] J. Pitman, “Some probabilistic aspects of set partitions,”Amer. Math. Monthly104(1997)201–209, Article [.pdf], Abstract[.txt], Preprint [.ps.Z], Math. Review.

Processes with drift

[1] J. Pitman and M. Yor, “Processus de Bessel, et mouvement brownien, avec drift,”C.R. Acad.Sc. Paris, Serie A291(1980) 151–153, Math. Review.

Random Permutations

[1] P. Diaconis, J. Fill, and J. Pitman, “Analysis of top in at random shuffles,”Combinatorics,Probability and Computing1 (1992) 135–155, Math. Review.

41

Random discrete distributions

[1] J. Pitman, “Random discrete distributions invariant under size-biased permutation,”Adv.Appl. Prob.28 (1996) 525–539, Preprint [.ps.Z], Math. Review.

[2] J. Pitman and M. Yor, “Random discrete distributions derived from self-similar random sets,”Electron. J. Probab.1 (1996) Paper 4, 1–28, Article.

[3] J. Pitman, “Poisson-Kingman partitions,” inScience and Statistics: A Festschrift for TerrySpeed, D. R. Goldstein, ed., vol. 30 ofLecture Notes-Monograph Series, pp. 1–34. Institute ofMathematical Statistics, Hayward, California, 2003. Article, Abstract[.txt], Preprint [.ps.Z].

Random forests

[1] J. Pitman, “Coalescent random forests,”J. Comb. Theory A.85 (1999) 165–193, Article[.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[2] J. Pitman, “Random mappings, forests and subsets associated with Abel-Cayley-Hurwitzmultinomial expansions,”Seminaire Lotharingien de CombinatoireIssue 46(2001) 45 pp.,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Random mappings

[1] D. Aldous and J. Pitman, “Brownian bridge asymptotics for random mappings,”RandomStructures and Algorithms5 (1994) 487–512, Math. Review.

[2] J. Pitman, “Random mappings, forests and subsets associated with Abel-Cayley-Hurwitzmultinomial expansions,”Seminaire Lotharingien de CombinatoireIssue 46(2001) 45 pp.,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] D. Aldous and J. Pitman, “Invariance principles for non-uniform random mappings andtrees,” inAsymptotic Combinatorics with Aplications in Mathematical Physics, V. Malyshevand A. M. Vershik, eds., pp. 113–147. Kluwer Academic Publishers, 2002. Abstract[.txt],Preprint [.ps.Z].

42

[4] D. Aldous and J. Pitman, “Two recursive decompositions of Brownian bridge related to theasymptotics of random mappings,” Tech. Rep. 595, Dept. Statistics, U.C. Berkeley, 2002.Abstract[.txt], Preprint [.ps.Z].

[5] D. Aldous and J. Pitman, “The asymptotic distribution of the diameter of a random mapping,”C.R. Acad. Sci. Paris, Ser. I334(2002) 1021–1024, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[6] D. Aldous, G. Miermont, and J. Pitman, “Brownian bridge asymptotics for randomp-mappings,” Tech. Rep. 624, Dept. Statistics, U.C. Berkeley, 2002. Abstract[.txt], Preprint[.ps.Z].

[7] J. Pitman, “Combinatorial Stochastic Processes,” Tech. Rep. 621, Dept. Statistics, U.C.Berkeley, 2002. Lecture notes for St. Flour course, July 2002. Corrections to version of July1,2002, Abstract[.txt], Preprint [.ps.Z].

Random measures

[1] P. Diaconis and J. Pitman, “Permutations, record values and random measures.” Unpublishedlecture notes. Dept. Statistics, U.C. Berkeley, 1986.

Random scaling

[1] J. Pitman and M. Yor, “Dilatations d’espace-temps, rearrangements des trajectoiresbrowniennes, et quelques extensions d’une identite de Knight,”C.R. Acad. Sci. Parist. 316,Serie I (1993) 723–726, Math. Review.

[2] J. Pitman and M. Yor, “Random Brownian scaling identities and splicing of Besselprocesses,”Ann. Probab.26 (1998) 1683–1702, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

43

Random subsets

[1] J. Pitman, “Random mappings, forests and subsets associated with Abel-Cayley-Hurwitzmultinomial expansions,”Seminaire Lotharingien de CombinatoireIssue 46(2001) 45 pp.,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Random times

[1] J. Pitman and T. Speed, “A note on random times,”Stoch. Proc. Appl.1 (1973) 369–374,Math. Review.

Random trees and forests

[1] J. Pitman, “The SDE solved by local times of a Brownian excursion or bridge derived fromthe height profile of a random tree or forest,”Ann. Probab.27 (1999) 261–283, Article [.pdf],Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[2] D. Aldous and J. Pitman, “A family of random trees with random edge lengths,”RandomStructures and Algorithms15 (1999) 176–195, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] M. Camarri and J. Pitman, “Limit distributions and random trees derived from the birthdayproblem with unequal probabilities,”Electron. J. Probab.5 (2000) Paper 2, 1–18, Article,Math. Review.

[4] J. Bennies and J. Pitman, “Asymptotics of the Hurwitz binomial distribution related to mixedPoisson Galton-Watson trees,”Combinatorics, Probability and Computing10 (2001)203–211, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[5] D. Aldous and J. Pitman, “Invariance principles for non-uniform random mappings andtrees,” inAsymptotic Combinatorics with Aplications in Mathematical Physics, V. Malyshevand A. M. Vershik, eds., pp. 113–147. Kluwer Academic Publishers, 2002. Abstract[.txt],Preprint [.ps.Z].

[6] J. Pitman, “Combinatorial Stochastic Processes,” Tech. Rep. 621, Dept. Statistics, U.C.Berkeley, 2002. Lecture notes for St. Flour course, July 2002. Corrections to version of July1,2002, Abstract[.txt], Preprint [.ps.Z].

44

Random walks

[1] P. Greenwood and J. Pitman, “Fluctuation identities for random walk by path decompositionat the maximum,”Advances in Applied Probability12 (1980) 291–293.

[2] J. Pitman, “Enumerations of trees and forests related to branching processes and randomwalks,” in Microsurveys in Discrete Probability, D. Aldous and J. Propp, eds., no. 41 inDIMACS Ser. Discrete Math. Theoret. Comp. Sci, pp. 163–180. Amer. Math. Soc.,Providence RI, 1998. Abstract[.txt], Preprint [.ps.Z], Math. Review.

Ranked functionals

[1] J. Pitman and M. Yor, “Ranked functionals of Brownian excursions,”C.R. Acad. Sci. Parist.326, Serie I (1998) 93–97, Article [.pdf], ScienceDirect, Math. Review.

[2] J. Pitman and M. Yor, “On the distribution of ranked heights of excursions of a Brownianbridge,”Ann. Probab.29 (2001) 361–384, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

Rates of convergence

[1] J. Pitman, “Uniform rates of convergence for Markov chain transition probabilities,”Z.Wahrsch. Verw. Gebiete29 (1974) 193–227, Math. Review.

[2] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

Rational maps

[1] J. Pitman and M. Yor, “Some properties of the arc sine law related to its invariance under afamily of rational maps,” Tech. Rep. 558, Dept. Statistics, U.C. Berkeley, 1999.Abstract[.txt], Preprint [.ps.Z].

45

Rational rotations

[1] L. Dubins and J. Pitman, “A pointwise ergodic theorem for the group of rational rotations,”Trans. Amer. Math. Soc.251(1980) 299–308, Math. Review.

Ray-Knight theorems

[1] J. Pitman and M. Yor, “A decomposition of Bessel bridges,”Z. Wahrsch. Verw. Gebiete59(1982) 425–457, Math. Review.

[2] J. Pitman, “Cyclically stationary Brownian local time processes,”Probab. Th. Rel. Fields106(1996) 299–329, Article [.ps.Z], SpringerLink, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] J. Pitman, “The SDE solved by local times of a Brownian excursion or bridge derived fromthe height profile of a random tree or forest,”Ann. Probab.27 (1999) 261–283, Article [.pdf],Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Records

[1] P. Diaconis and J. Pitman, “Permutations, record values and random measures.” Unpublishedlecture notes. Dept. Statistics, U.C. Berkeley, 1986.

Reflection

[1] J. Pitman, “One-dimensional Brownian motion and the three-dimensional Bessel process,”Advances in Applied Probability7 (1975) 511–526, Math. Review.

[2] S. Asmussen, P. Glynn, and J. Pitman, “Discretization error in simulation of one-dimensionalreflecting Brownian motion,”Ann. Applied Prob.5 (1995) 875–896, Math. Review.

[3] H. Dette, J. Fill, J. Pitman, and W. Studden, “Wall and Siegmund duality relations for birthand death chains with reflecting barrier,”Journal of Theoretical Probability10 (1997)349–374, Preprint [.ps.Z], Math. Review.

46

Regenerative sets

[1] P. Greenwood and J. Pitman, “Construction of local time and Poisson point processes fromnested arrays,”Journal of the London Mathematical Society22 (1980) 182–192, Math.Review.

[2] J. Bertoin and J. Pitman, “Two coalescents derived from the ranges of stable subordinators,”Electron. J. Probab.5 (2000) no. 7, 17 pp., Article, Math. Review.

Riemmann zeta function

[1] P. Biane, J. Pitman, and M. Yor, “Probability laws related to the Jacobi theta and Riemannzeta functions, and Brownian excursions,”Bull. Amer. Math. Soc.38 (2001) 435–465, Article,Math. Review.

Rifle shufles

[1] P. Diaconis, M. McGrath, and J. Pitman, “Riffle shuffles, cycles and descents,”Combinatorica15 (1995) 11–29, Math. Review.

Sampling at uniform times

[1] J. Pitman, “Brownian motion, bridge, excursion and meander characterized by sampling atindependent uniform times,”Electron. J. Probab.4 (1999) Paper 11, 1–33, Article, Math.Review.

47

Scholarly communication

[1] J. Pitman, “Two rules of scholarly communication: publish for the public, and keep thejournals.” Submitted to Notices AMS, 2002. Article.

[2] J. Pitman, “The digital revolution in scholarly communication.” 2002. Article.

[3] J. Pitman, “The Mathematics Survey Proposal.” Submitted to Notices AMS, 2002. Article.

[4] J. Pitman, “The future of IMS journals,”IMS Bulletin32 (2003) Issue 1, p. 1, Article.

Self-similar processes

[1] J. Pitman and M. Yor, “Random discrete distributions derived from self-similar random sets,”Electron. J. Probab.1 (1996) Paper 4, 1–28, Article.

[2] J. Pitman and M. Yor, “On the distribution of ranked heights of excursions of a Brownianbridge,”Ann. Probab.29 (2001) 361–384, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

[3] M. Jeanblanc, J. Pitman, and M. Yor, “Self-similar processes with independent incrementsassociated with Levy and Bessel processes,”Stochastic Processes Appl.100(2002) 223–232,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Self-similar sets

[1] J. Pitman and M. Yor, “Random discrete distributions derived from self-similar random sets,”Electron. J. Probab.1 (1996) Paper 4, 1–28, Article.

Set partitions

[1] J. Pitman, “Some probabilistic aspects of set partitions,”Amer. Math. Monthly104(1997)201–209, Article [.pdf], Abstract[.txt], Preprint [.ps.Z], Math. Review.

48

Simulation

[1] S. Asmussen, P. Glynn, and J. Pitman, “Discretization error in simulation of one-dimensionalreflecting Brownian motion,”Ann. Applied Prob.5 (1995) 875–896, Math. Review.

Singular measure

[1] D. Freedman and J. Pitman, “A singular measure which is locally uniform,”Proc. Amer.Math. Soc.108(1990) 371–381, Math. Review.

Size-biased permutation

[1] J. Pitman, “Random discrete distributions invariant under size-biased permutation,”Adv.Appl. Prob.28 (1996) 525–539, Preprint [.ps.Z], Math. Review.

Size-biased sampling

[1] M. Perman, J. Pitman, and M. Yor, “Size-biased Sampling of Poisson Point Processes andExcursions,”Probab. Th. Rel. Fields92 (1992) 21–39, Math. Review.

[2] J. Pitman, “Random discrete distributions invariant under size-biased permutation,”Adv.Appl. Prob.28 (1996) 525–539, Preprint [.ps.Z], Math. Review.

Skew fields

[1] L. Dubins and J. Pitman, “A maximal inequality for skew fields,”Z. Wahrsch. Verw. Gebiete52 (1980) 219–227, Math. Review.

49

Species sampling

[1] J. Pitman, “Some developments of the Blackwell-MacQueen urn scheme,” inStatistics,Probability and Game Theory; Papers in honor of David Blackwell, T. F. et al., ed., vol. 30 ofLecture Notes-Monograph Series, pp. 245–267. Institute of Mathematical Statistics,Hayward, California, 1996. Preprint [.ps.Z], Math. Review.

[2] B. Hansen and J. Pitman, “Prediction rules and exchangeable sequences related to speciessampling,”Stat. and Prob. Letters46 (2000) 251–256, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Splicing paths

[1] J. Pitman and M. Yor, “Random Brownian scaling identities and splicing of Besselprocesses,”Ann. Probab.26 (1998) 1683–1702, Article [.pdf], Project Euclid, Abstract[.txt],Preprint [.ps.Z], Math. Review.

Split-and-merge transformations

[1] J. Pitman, “Poisson-Dirichlet and GEM invariant distributions for split-and-mergetransformations of an interval partition,”Combinatorics, Probability and Computing11(2002) 501–514, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Stable Ornstein-Uhlenbeck processes

[1] S. Evans and J. Pitman, “Stationary Markov processes related to stable Ornstein-Uhlenbeckprocesses and the additive coalescent,”Stochastic Processes Appl.77 (1998) 175–185,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

50

Stable subordinators

[1] J. Pitman and M. Yor, “Arcsine laws and interval partitions derived from a stablesubordinator,”Proc. London Math. Soc. (3)65 (1992) 326–356, Math. Review.

[2] J. Pitman, “Partition structures derived from Brownian motion and stable subordinators,”Bernoulli3 (1997) 79–96, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] J. Pitman and M. Yor, “The two-parameter Poisson-Dirichlet distribution derived from astable subordinator,”Ann. Probab.25 (1997) 855–900, Article [.pdf], Project Euclid,Abstract[.txt], Preprint [.ps.Z], Math. Review.

[4] J. Pitman and M. Yor, “On the relative lengths of excursions derived from a stablesubordinator,” inSeminaire de Probabilites XXXI, vol. 1655 ofLecture Notes in Math.,pp. 287–305. Springer, 1997. Abstract[.txt], Preprint [.ps.Z], Math. Review.

[5] J. Bertoin and J. Pitman, “Two coalescents derived from the ranges of stable subordinators,”Electron. J. Probab.5 (2000) no. 7, 17 pp., Article, Math. Review.

[6] J. Pitman, “Combinatorial Stochastic Processes,” Tech. Rep. 621, Dept. Statistics, U.C.Berkeley, 2002. Lecture notes for St. Flour course, July 2002. Corrections to version of July1,2002, Abstract[.txt], Preprint [.ps.Z].

Stationary processes

[1] J. Pitman, “Stationary excursions,” inSeminaire de Probabilites XXI, vol. 1247 ofLectureNotes in Math., pp. 289–302. Springer, 1986. Math. Review.

[2] S. Evans and J. Pitman, “Stationary Markov processes related to stable Ornstein-Uhlenbeckprocesses and the additive coalescent,”Stochastic Processes Appl.77 (1998) 175–185,Article [.pdf], ScienceDirect, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Stochastic differential equations

[1] J. Pitman, “The SDE solved by local times of a Brownian excursion or bridge derived fromthe height profile of a random tree or forest,”Ann. Probab.27 (1999) 261–283, Article [.pdf],Project Euclid, Abstract[.txt], Preprint [.ps.Z], Math. Review.

51

Stopping time

[1] J. Pitman and T. Speed, “A note on random times,”Stoch. Proc. Appl.1 (1973) 369–374,Math. Review.

[2] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

[3] J. Pitman, “An identity for stopping times of a Markov Process,” inStudies in Probability andStatistics, pp. 41–57. Jerusalem Academic Press, 1974. Math. Review.

[4] S. Evans and J. Pitman, “Stopped Markov chains with stationary occupation times,”Probab.Th. Rel. Fields109(1997) 425–433, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Stopping times

[1] J. Pitman and T. Speed, “A note on random times,”Stoch. Proc. Appl.1 (1973) 369–374,Math. Review.

[2] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

[3] S. Evans and J. Pitman, “Stopped Markov chains with stationary occupation times,”Probab.Th. Rel. Fields109(1997) 425–433, Abstract[.txt], Preprint [.ps.Z], Math. Review.

Transition probabilities

[1] J. Pitman, “Uniform rates of convergence for Markov chain transition probabilities,”Z.Wahrsch. Verw. Gebiete29 (1974) 193–227, Math. Review.

[2] J. Pitman,Stopping time identities and limit theorems for Markov chains. PhD thesis, Dept.Prob. and Stat., University of Sheffield, 1974.

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Tree-valued Markov chains

[1] D. Aldous and J. Pitman, “Tree-valued Markov chains derived from Galton-Watsonprocesses,”Ann. Inst. Henri Poincare34 (1998) 637–686, Article [.pdf], ScienceDirect,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Trees and forests

[1] J. Pitman, “Enumerations of trees and forests related to branching processes and randomwalks,” in Microsurveys in Discrete Probability, D. Aldous and J. Propp, eds., no. 41 inDIMACS Ser. Discrete Math. Theoret. Comp. Sci, pp. 163–180. Amer. Math. Soc.,Providence RI, 1998. Abstract[.txt], Preprint [.ps.Z], Math. Review.

Two-parameter family

[1] J. Pitman, “The two-parameter generalization of Ewens’ random partition structure,” Tech.Rep. 345, Dept. Statistics, U.C. Berkeley, 1992.

[2] J. Pitman and M. Yor, “The two-parameter Poisson-Dirichlet distribution derived from astable subordinator,”Ann. Probab.25 (1997) 855–900, Article [.pdf], Project Euclid,Abstract[.txt], Preprint [.ps.Z], Math. Review.

Undergraduate text

[1] J. Pitman,Probability. Springer-Verlag, New York, 1993.

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Urn schemes

[1] J. Pitman, “Some developments of the Blackwell-MacQueen urn scheme,” inStatistics,Probability and Game Theory; Papers in honor of David Blackwell, T. F. et al., ed., vol. 30 ofLecture Notes-Monograph Series, pp. 245–267. Institute of Mathematical Statistics,Hayward, California, 1996. Preprint [.ps.Z], Math. Review.

Walshs Brownian motions

[1] M. Barlow, J. Pitman, and M. Yor, “On Walsh’s Brownian motions,” inSeminaire deProbabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 275–293. Springer, 1989. Math.Review.

[2] M. Barlow, J. Pitman, and M. Yor, “Une extension multidimensionnelle de la loi de l’arcsinus,” inSeminaire de Probabilites XXIII, vol. 1372 ofLecture Notes in Math., pp. 294–314.Springer, 1989. Math. Review.

Windings

[1] J. Pitman and M. Yor, “The asymptotic joint distribution of windings of planar Brownianmotion,” Bulletin of the American Mathematical Society10 (1984) 109–111, Math. Review.

[2] J. Pitman and M. Yor, “Asymptotic laws of planar Brownian motion,”Annals of Probability14 (1986) 733–779, Article [.pdf], Math. Review.

[3] J. Pitman and M. Yor, “Complementsa l’etude asymptotique des nombres de tours dumouvement brownien complexe autour d’un nombre fini de points,”C.R. Acad. Sc. Paris,Serie I 305(1987) 757–760, Math. Review.

[4] J. Pitman and M. Yor, “Further asymptotic laws of planar Brownian motion,”Annals ofProbability17 (1989) 965–1011, Article [.pdf], Math. Review.

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Zero-one law

[1] D. Aldous and J. Pitman, “On the zero-one law for exchangeable events,”Annals ofProbability7 (1979) 704–723, Math. Review.

Zero sets

[1] J. Pitman, “Partition structures derived from Brownian motion and stable subordinators,”Bernoulli3 (1997) 79–96, Abstract[.txt], Preprint [.ps.Z], Math. Review.

[2] J. Pitman and M. Yor, “On the lengths of excursions of some Markov processes,” inSeminaire de Probabilites XXXI, vol. 1655 ofLecture Notes in Math., pp. 272–286. Springer,1997. Abstract[.txt], Preprint [.ps.Z], Math. Review.

[3] J. Pitman and M. Yor, “On the relative lengths of excursions derived from a stablesubordinator,” inSeminaire de Probabilites XXXI, vol. 1655 ofLecture Notes in Math.,pp. 287–305. Springer, 1997. Abstract[.txt], Preprint [.ps.Z], Math. Review.

de Finettis theorem

[1] J. Pitman, “An extension of de Finetti’s theorem,”Advances in Applied Probability10 (1978)268–270.

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