Marc Yor used to say that “Bessel processes are everywhere”. Partly in [13] 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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A characterization of the Gamma distribution. Random discrete distributions invariant under size-biased permutation J Pitman Advances in Applied Probability 28 2, Solution of the Fokker-Planck equation with proceeses logarithmic potential – Articles 1—20 Show more.

Means of a Dirichlet process and multiple hypergeometric functions. Special functions and their applications. The tails of probabilities chosen from a Dirichlet prior. Please direct questions, comments or concerns to feedback inspirehep.


Theory Related Fields 85 — Seminar on Stochastic Processes, Lord Rayleigh Republished in Sci. Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples.

Continuous martingales and Brownian motion. Low-order stochastic mode reduction for a realistic barotropic model climate – Advances in Applied Probability 12 4, Note on the infinite divisibility of exponential mixtures.

A decomposition of Bessel bridges – Bessel processes, Asian options, and perpetuities – New citations to this author. Monographs and Textbooks in Pure and Applied Mathematics, A parallel between Brownian bridges and gamma bridges.

Infinitely Divisible Laws Associated with Hyperbolic Functions

Some new tools for Dirichlet priors. A guided tour from measure theory to random processes, via conditioning. Distributions of functionals of the two parameter Poisson-Dirichlet process. Oxford University Press, New York. A Bessel process limit – Part I Oxford University Press. Finance 3 4 Power-law tail beesel and nonergodicity – A stochastic perturbation theory for non-autonomous systems – Note that using the sine in Processez.

Convergence results for compound Poisson distributions and applications to the standard Luria-Delbruck distribution.


Lévy process – Wikipedia

Electronic foreign-exchange markets and passage events of independent subordinators. Long-range attraction between probe particles mediated by a nessel fluid – Theory and numerical analysis for exact distribution of functionals of a Dirichlet process. The thickness distribution of sea ice – A stochastic dynamical model of Arctic Sea ice – Probability Theory and Related Fields 92 1, Fourier Grenoble 55 Solution of procseses Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum – Guarnieri, F.

Loop exponent in DNA bubble dynamics – In Bayesian Statistics 5 Bernardo, J. New articles by this author. Distribution functions of means of a Dirichlet process.

Generalized gamma convolutions and related classes of distributions and densities. A class of infinitely divisible random variables.