{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T07:01:44Z","timestamp":1791529304681,"version":"4.3.4"},"reference-count":14,"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":"We propose a two-urn model of P\u00f3lya type as follows. There are two urns, urnA<\/jats:italic>and urnB<\/jats:italic>. At the beginning, urnA<\/jats:italic>containsr<\/jats:italic>A<\/jats:italic><\/jats:sub>red andw<\/jats:italic>A<\/jats:italic><\/jats:sub>white balls and urnB<\/jats:italic>containsr<\/jats:italic>B<\/jats:italic><\/jats:sub>red andw<\/jats:italic>B<\/jats:italic><\/jats:sub>white balls. We first drawm<\/jats:italic>balls from urnA<\/jats:italic>and note their colors, sayi<\/jats:italic>red andm<\/jats:italic>-i<\/jats:italic>white balls. The balls are returned to urnA<\/jats:italic>andbi<\/jats:italic>red andb<\/jats:italic>(m<\/jats:italic>-i<\/jats:italic>) white balls are added to urnB<\/jats:italic>. Next, we draw \u2113 balls from urnB<\/jats:italic>and note their colors, sayj<\/jats:italic>red and \u2113 -j<\/jats:italic>white balls. The balls are returned to urnB<\/jats:italic>andaj<\/jats:italic>red anda<\/jats:italic>(\u2113 -j<\/jats:italic>) white balls are added to urnA<\/jats:italic>. Repeat the above actionn<\/jats:italic>times and letX<\/jats:italic>n<\/jats:italic><\/jats:sub>be the fraction of red balls in urnA<\/jats:italic>andY<\/jats:italic>n<\/jats:italic><\/jats:sub>the fraction of red balls in urnB<\/jats:italic>. We first show that the expectations ofX<\/jats:italic>n<\/jats:italic><\/jats:sub>andY<\/jats:italic>n<\/jats:italic><\/jats:sub>have the same limit, and then use martingale theory to show thatX<\/jats:italic>n<\/jats:italic><\/jats:sub>andY<\/jats:italic>n<\/jats:italic><\/jats:sub>converge almost surely to the same limit.<\/jats:p>","DOI":"10.1239\/jap\/1402578645","type":"journal-article","created":{"date-parts":[[2014,6,12]],"date-time":"2014-06-12T13:18:54Z","timestamp":1402579134000},"page":"590-597","source":"Crossref","is-referenced-by-count":7,"title":["A New Two-Urn Model"],"prefix":"10.1017","volume":"51","author":[{"given":"May-Ru","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shoou-Ren","family":"Hsiau","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ting-Hsin","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S002190020001144X_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4140-9_14"},{"key":"S002190020001144X_ref9","volume-title":"Urn Models and Their Application","author":"Johnson","year":"1977"},{"key":"S002190020001144X_ref7","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1053003552"},{"key":"S002190020001144X_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-7152(89)90126-0"},{"key":"S002190020001144X_ref4","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1134587809"},{"key":"S002190020001144X_ref1","volume-title":"Measure Theory and Probability Theory","author":"Athreya","year":"2006"},{"key":"S002190020001144X_ref2","doi-asserted-by":"publisher","DOI":"10.1137\/0606041"},{"key":"S002190020001144X_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01046101"},{"key":"S002190020001144X_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02460937"},{"key":"S002190020001144X_ref12","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0096-3003(94)00153-U","article-title":"Urn model simulations of a sexually transmitted disease epidemic","volume":"71","author":"Martin","year":"1995","journal-title":"Appl. Math. Comput."},{"key":"S002190020001144X_ref5","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19230030407"},{"key":"S002190020001144X_ref11","volume-title":"P\u00f3lya Urn Models","author":"Mahmoud","year":"2009"},{"key":"S002190020001144X_ref14","unstructured":"[14] Renlund H. (2010). Generalized P\u00f3lya urns via stochastic approximation. Preprint, available at {http:\/\/arxiv.org\/abs\/1002.3716}."},{"key":"S002190020001144X_ref8","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994772"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002190020001144X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T09:45:27Z","timestamp":1746265527000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002190020001144X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":14,"aliases":["10.1017\/s002190020001144x"],"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S002190020001144X"],"URL":"https:\/\/doi.org\/10.1239\/jap\/1402578645","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}