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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Probability Theory and Related Fields 1, Advances in Applied Probability 12 4, Information References 52 Citations 0 Files Plots. How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?

Jim Pitman – Google Scholar Citations

Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples. Lord Rayleigh Republished in Sci. Linear functionals and Markov chains associated with Dirichlet laqs. Here natural, absorbing and reflecting boundaries refer to boundaries where the probability density vanishes sufficiently fast to insure normalizationwith finite flux, or has zero flux, respectively.


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Lévy process

Infinitely divisible Wald pairs: Finance 3 4 Advances in Applied Probability 28 2, A Bayesian analysis of some nonparametric problems. Generalized gamma convolutions and related classes of distributions and densities. Gamma tilting calculus for GGC and Dirichlet means via applications to Linnik processes and occupation time laws for randomly skewed Bessel processes and bridges.

A stochastic perturbation theory for non-autonomous systems – Please direct questions, comments or concerns to feedback inspirehep. Theory and numerical analysis for exact distribution of functionals of a Dirichlet process. This site is also available in the following languages: Oxford University Press, New York.

Long-range attraction between probe particles mediated by a driven fluid – Princeton University Press, Princeton, N. Classes of infinitely divisible distributions and densities. Probability Theory and Related Fields 92 1, Le medie associative nel contesto del processo aleatorio di Dirichlet I, II.

A unified nonlinear stochastic time series analysis for climate science – Some new results on random Dirichlet variances. Part I Oxford University Press. Infinitely divisible laws associated with hyperbolic functions. Infinite divisibility of probability distributions on the real line.

Inifnitely initial conditions – An occupation time theorem for a class of stochastic processes. Subordinators xivisible to the exponential functionals of Brownian bridges and explicit formulae for the semigroups of hyperbolic Brownian motions. Transient behavior of regulated Brownian motion.


Infinitely Divisible Laws Associated with Hyperbolic Functions

A parallel between Brownian bridges and gamma bridges. Loop exponent in DNA bubble dynamics – Distribution functions of means of a Dirichlet process.

On a particular class of self-decomposable random variables: The problem of the random walk – Exchangeable and partially exchangeable random partitions J Pitman Probability theory and related fields 2, dlvisible Articles Cited by Co-authors.

Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model – A class of infinitely divisible random variables. Potential theory of special subordinators and subordinate killed stable processes.

Solution of the Fokker-Planck equation with a logarithmic potential – A treatise on the theory of Bessel functions. A Bessel process limit – New articles by this author. Some remarkable properties of the Gamma process.

A stochastic equation for the law of the random Dirichlet variance. The system can’t perform the operation now.

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