{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:41:25Z","timestamp":1682502085726},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>We propose a two-urn model of P\u00f3lya type as follows. There are two urns, urn <jats:italic>A<\/jats:italic> and urn <jats:italic>B<\/jats:italic>. At the beginning, urn <jats:italic>A<\/jats:italic> contains <jats:italic>r<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>A<\/jats:italic>\n               <\/jats:sub> red and <jats:italic>w<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>A<\/jats:italic>\n               <\/jats:sub> white balls and urn <jats:italic>B<\/jats:italic> contains <jats:italic>r<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>B<\/jats:italic>\n               <\/jats:sub> red and <jats:italic>w<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>B<\/jats:italic>\n               <\/jats:sub> white balls. We first draw <jats:italic>m<\/jats:italic> balls from urn <jats:italic>A<\/jats:italic> and note their colors, say <jats:italic>i<\/jats:italic> red and <jats:italic>m<\/jats:italic> - <jats:italic>i<\/jats:italic>\nwhite balls. The balls are returned to urn <jats:italic>A<\/jats:italic> and <jats:italic>bi<\/jats:italic> red and <jats:italic>b<\/jats:italic>(<jats:italic>m<\/jats:italic> - <jats:italic>i<\/jats:italic>) white balls are added to urn <jats:italic>B<\/jats:italic>. Next, we draw \u2113 balls from urn <jats:italic>B<\/jats:italic> and note their colors, say <jats:italic>j<\/jats:italic> red and \u2113 - <jats:italic>j<\/jats:italic> white balls. The balls are returned to urn <jats:italic>B<\/jats:italic> and <jats:italic>aj<\/jats:italic> red and <jats:italic>a<\/jats:italic>(\u2113 - <jats:italic>j<\/jats:italic>) white balls are added to urn <jats:italic>A<\/jats:italic>. Repeat the above action <jats:italic>n<\/jats:italic> times and let <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> be the fraction of red balls in urn <jats:italic>A<\/jats:italic> and <jats:italic>Y<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> the fraction of red balls in urn <jats:italic>B<\/jats:italic>. We first show that the expectations of <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> and <jats:italic>Y<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> have the same limit, and then use martingale theory to show that <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> and <jats:italic>Y<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> converge almost surely to the same limit.<\/jats:p>","DOI":"10.1017\/s002190020001144x","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:10Z","timestamp":1459263070000},"page":"590-597","source":"Crossref","is-referenced-by-count":2,"title":["A New Two-Urn Model"],"prefix":"10.1017","volume":"51","author":[{"given":"May-Ru","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shoou-Ren","family":"Hsiau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ting-Hsin","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S002190020001144X_ref9","volume-title":"Urn Models and Their Application","year":"1977"},{"key":"S002190020001144X_ref8","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994772"},{"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_ref5","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19230030407"},{"key":"S002190020001144X_ref4","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1134587809"},{"key":"S002190020001144X_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4140-9_14"},{"key":"S002190020001144X_ref2","doi-asserted-by":"publisher","DOI":"10.1137\/0606041"},{"key":"S002190020001144X_ref1","volume-title":"Measure Theory and Probability Theory","year":"2006"},{"key":"S002190020001144X_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01046101"},{"key":"S002190020001144X_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(94)00153-U"},{"key":"S002190020001144X_ref11","volume-title":"P\u00f3lya Urn Models","year":"2009"},{"key":"S002190020001144X_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02460937"}],"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":[[2023,4,26]],"date-time":"2023-04-26T09:09:28Z","timestamp":1682500168000},"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":13,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S002190020001144X"],"URL":"https:\/\/doi.org\/10.1017\/s002190020001144x","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}