Journal of Applied Probability

Dirichlet random walks

Gérard Letac and Mauro Piccioni

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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.

Article information

J. Appl. Probab., Volume 51, Number 4 (2014), 1081-1099.

First available in Project Euclid: 20 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60D99: None of the above, but in this section 60F99: None of the above, but in this section

Dirichlet process Stieltjes transform random flight distributions in a sphere hyperuniformity infinite divisibility in the sense of Dirichlet


Letac, Gérard; Piccioni, Mauro. Dirichlet random walks. J. Appl. Probab. 51 (2014), no. 4, 1081--1099.

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