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December 2014 Dirichlet random walks
Gérard Letac, Mauro Piccioni
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J. Appl. Probab. 51(4): 1081-1099 (December 2014).

Abstract

This paper provides tools for the study of the Dirichlet random walk in Rd. We compute explicitly, for a number of cases, the distribution of the random variable W using a form of Stieltjes transform of W instead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2010), (2011). We extend our results to the study of the limits of the Dirichlet random walk when the number of added terms goes to ∞, interpreting the results in terms of an integral by a Dirichlet process. We introduce the ideas of Dirichlet semigroups and Dirichlet infinite divisibility and characterize these infinite divisible distributions in the sense of Dirichlet when they are concentrated on the unit sphere of Rd.

Citation

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Gérard Letac. Mauro Piccioni. "Dirichlet random walks." J. Appl. Probab. 51 (4) 1081 - 1099, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 1320.60108
MathSciNet: MR3301290

Subjects:
Primary: 60D99, 60F99

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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