Marc Yor used to say that “Bessel processes are everywhere”. Partly in  J. Pitman, M. Yor, Bessel processes and infinitely divisible laws. BESSEL PROCESSES AND INFINITELY DIVISIBLE LAWS by. Jim PITMAN and Marc YOR (n). 1. INTRODUCTION. In recent years there has been a renewed. Theorem (Lévy–Khintchine formula) A probability law µ of a real- . To conclude our introduction to Lévy processes and infinite divisible distribu- tions, let us .. for x ∈ R where α,δ > 0, β ≤ |α| and K1(x) is the modified Bessel function of.
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Monographs and Textbooks in Pure and Applied Mathematics, The tails of probabilities chosen from a Dirichlet prior.
Some remarks on the Rayleigh process – Spectral expansions for Asian average price options – Decomposing the Brownian path – Electronic foreign-exchange markets and passage events of independent subordinators.
A characterization of the Gamma distribution.
Nonzero initial conditions – On a stochastic difference equation and a representation of non-negative infinitely divisible random variables. Nonlinear threshold behavior during the loss of Arctic Sea ice – Potential theory of special subordinators and subordinate killed stable processes. Random discrete distributions invariant under size-biased permutation J Pitman Advances in Applied Probability 28 2, Advances in Applied Probability 12 4, The spectral representation of Bessel processes with constant drift: Loop exponent in DNA bubble dynamics – On the Markov—Krein identity and quasi—invariance of the gamma process.
First-passage and first-exit times of a Bessel-like stochastic process – Long-range attraction between probe particles mediated by a driven fluid – Weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem – A unified nonlinear stochastic time series analysis for climate science – On the resultant of a large number of vibrations of the same pitch and of arbitrary phase – Lord Rayleigh Note that using the sine in Eq.
The parabolic differential equations and the associated semi-groups of transformations – In Bayesian Statistics 5 Bernardo, J.
CiteSeerX — Infinitely Divisible Laws Associated With Hyperbolic Functions
Translated from the Japanese original. The transition function of a Fleming-Viot process Ann.
Continuous martingales and Brownian motion. Statistics, UC Berkeley, diviisible Multiplicative stochastic processes in statistical physics – Schenzle, A. Transient behavior of regulated Brownian motion.
Generalized gamma convolutions and complete monotonicity. Some classes of multivariate infinitely divisible distribution admitting stochastic integral representations Bernoulli12p.
Social 239— A survey and some generalizations of Bessel processes – Distributions of functionals of the two parameter Poisson-Dirichlet process. The system can’t perform the operation now.
Jim Pitman – Google 学术搜索引用
A Bayesian analysis of some nonparametric problems. A theory of the term structure of interest rates – Linear functionals and Markov chains associated with Dirichlet processes. Here natural, absorbing and reflecting boundaries refer to boundaries where the probability density vanishes sufficiently fast to insure normalizationwith finite flux, or ininitely zero flux, respectively. Their combined citations are counted only for the first article. Starting at the origin – Bernoulli 9 2 New citations to this author.
Extended Thorin classes and stochastic integrals. Some new results on random Dirichlet variances. Infinitely divisible Wald pairs: Articles Cited by Co-authors. Theory Related Fields 85 —