{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T06:44:12Z","timestamp":1791528252189,"version":"4.3.4"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T00:00:00Z","timestamp":1517270400000},"content-version":"unspecified","delay-in-days":1156,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Probability"],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>This paper provides tools for the study of the Dirichlet random walk in <jats:bold>R<\/jats:bold><jats:sup><jats:italic>d<\/jats:italic><\/jats:sup>. We compute explicitly, for a number of cases, the distribution of the random variable <jats:italic>W<\/jats:italic> using a form of Stieltjes transform of <jats:italic>W<\/jats:italic> 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 Ca\u00ebr (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 \u221e, 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 <jats:bold>R<\/jats:bold><jats:sup><jats:italic>d<\/jats:italic><\/jats:sup>.<\/jats:p>","DOI":"10.1239\/jap\/1421763329","type":"journal-article","created":{"date-parts":[[2015,1,20]],"date-time":"2015-01-20T14:15:34Z","timestamp":1421763334000},"page":"1081-1099","source":"Crossref","is-referenced-by-count":11,"title":["Dirichlet Random Walks"],"prefix":"10.1017","volume":"51","author":[{"given":"G\u00e9rard","family":"Letac","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mauro","family":"Piccioni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"S0021900200120789_ref2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-2011-079-2"},{"key":"S0021900200120789_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/09-SS041"},{"key":"S0021900200120789_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-011-0245-4"},{"key":"S0021900200120789_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988865"},{"key":"S0021900200120789_ref4","first-page":"95","article-title":"A general approach to Bayesian analysis of nonparametric problems. The associative mean values within the framework of the Dirichlet process. II","volume":"2","author":"Cifarelli","year":"1979","journal-title":"Riv. Mat. Sci. Econom. Social"},{"key":"S0021900200120789_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-010-0015-8"},{"key":"S0021900200120789_ref1","doi-asserted-by":"publisher","DOI":"10.1080\/17442500903359163"},{"key":"S0021900200120789_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347509"},{"key":"S0021900200120789_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s11203-005-6068-7"},{"key":"S0021900200120789_ref7","first-page":"61","article-title":"On the distribution of random Dirichlet Jumps","volume":"64","author":"Hjort","year":"2006","journal-title":"Metron"},{"key":"S0021900200120789_ref12","first-page":"639","article-title":"A constructive definition of Dirichlet priors","volume":"4","author":"Sethuraman","year":"1994","journal-title":"Statistica Sinica"},{"key":"S0021900200120789_ref8","first-page":"33","article-title":"The explicit probability distribution of a six-dimensional random flight","volume":"15","author":"Kolesnik","year":"2009","journal-title":"Theory Stoch. Process."}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200120789","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,21]],"date-time":"2019-04-21T21:51:47Z","timestamp":1555883507000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200120789\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":12,"aliases":["10.1017\/s0021900200011992"],"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["S0021900200120789"],"URL":"https:\/\/doi.org\/10.1239\/jap\/1421763329","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}