This paper provides tools for the study of the Dirichlet random walk inRd. We compute explicitly, for a number of cases, thedistribution of the random variable W using a form of Stieltjestransform of W instead of the Laplace transform, replacing the Besselfunctions with hypergeometric functions. This enables us to simplify someexisting results, in particular, some of the proofs by Le Caër (2010),(2011). We extend our results to the study of the limits of the Dirichletrandom walk when the number of added terms goes to ∞, interpreting theresults in terms of an integral by a Dirichlet process. We introduce the ideasof Dirichlet semigroups and Dirichlet infinite divisibility and characterizethese infinite divisible distributions in the sense of Dirichlet when they areconcentrated on the unit sphere of Rd.
"Dirichlet random walks." J. Appl. Probab. 51 (4) 1081 - 1099, December 2014.