Name
Abstract | ||
|---|---|---|
This paper provides tools for the study of the Dirichlet random walk in R-d. 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 Caer (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 infinity, 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 R-d. |
Year | Venue | Keywords |
|---|---|---|
2014 | JOURNAL OF APPLIED PROBABILITY | Dirichlet process, Stieltjes transform, random flight, distributions in a sphere, hyperuniformity, infinite divisibility in the sense of Dirichlet |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Dirichlet process,Random walk,Dirichlet distribution,Mathematics,Stieltjes transform | Journal | 51 |
Issue | ISSN | Citations |
4 | 0021-9002 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gérard Letac | 1 | 4 | 2.50 |
| Mauro Piccioni | 2 | 4 | 1.90 |