{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T07:24:48Z","timestamp":1791530688807,"version":"4.3.4"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2016,2,19]],"date-time":"2016-02-19T00:00:00Z","timestamp":1455840000000},"content-version":"unspecified","delay-in-days":628,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Probability"],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>We characterise the class of distributions of random stochastic matrices <jats:italic>X<\/jats:italic> with the property that the products <jats:italic>X<\/jats:italic>(<jats:italic>n<\/jats:italic>)<jats:italic>X<\/jats:italic>(<jats:italic>n<\/jats:italic> \u2212 1) \u00b7 \u00b7 \u00b7 <jats:italic>X<\/jats:italic>(1) of independent and identically distributed copies <jats:italic>X<\/jats:italic>(<jats:italic>k<\/jats:italic>) of <jats:italic>X<\/jats:italic> converge almost surely as <jats:italic>n<\/jats:italic> \u2192 \u221e and the limit is Dirichlet distributed. This extends a result by Chamayou and Letac (1994) and is illustrated by several examples that are of interest in applications.<\/jats:p>","DOI":"10.1239\/jap\/1402578642","type":"journal-article","created":{"date-parts":[[2014,6,12]],"date-time":"2014-06-12T13:18:54Z","timestamp":1402579134000},"page":"542-555","source":"Crossref","is-referenced-by-count":6,"title":["A Characterisation of Transient Random Walks on Stochastic Matrices with Dirichlet Distributed Limits"],"prefix":"10.1017","volume":"51","author":[{"given":"S.","family":"McKinlay","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S0021900200011414_ref25","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1993.1050"},{"key":"S0021900200011414_ref24","doi-asserted-by":"publisher","DOI":"10.2307\/3214475"},{"key":"S0021900200011414_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100019563"},{"key":"S0021900200011414_ref19","doi-asserted-by":"publisher","DOI":"10.1002\/9781119995784"},{"key":"S0021900200011414_ref17","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728549"},{"key":"S0021900200011414_ref15","volume-title":"Human Genetics","author":"Li","year":"1961"},{"key":"S0021900200011414_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00535158"},{"key":"S0021900200011414_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-77548-7"},{"key":"S0021900200011414_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177705909"},{"key":"S0021900200011414_ref6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988865"},{"key":"S0021900200011414_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9172-2"},{"key":"S0021900200011414_ref2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-54-02148-1"},{"key":"S0021900200011414_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-4109-0"},{"key":"S0021900200011414_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(00)00114-0"},{"key":"S0021900200011414_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532045"},{"key":"S0021900200011414_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/09-AIHP211"},{"key":"S0021900200011414_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-28003-0"},{"key":"S0021900200011414_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(63)90071-4"},{"key":"S0021900200011414_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00531427"},{"key":"S0021900200011414_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(65)90064-8"},{"key":"S0021900200011414_ref8","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1997.0576"},{"key":"S0021900200011414_ref14","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1035228119"},{"key":"S0021900200011414_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(02)00027-5"},{"key":"S0021900200011414_ref18","volume-title":"Topics in Products of Random Matrices","author":"Mukherjea","year":"2000"},{"key":"S0021900200011414_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01046992"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200011414","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T20:00:29Z","timestamp":1555963229000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200011414\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":25,"aliases":["10.1017\/s0021900200011414"],"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S0021900200011414"],"URL":"https:\/\/doi.org\/10.1239\/jap\/1402578642","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}