{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:40:55Z","timestamp":1682494855190},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p>For a sequence of finite state space birth\u2013death processes, each having a single absorbing state, we show that, under certain conditions, as the size of the state space tends to infinity, the quasistationary distributions converge to the stationary distribution of a limiting infinite state space birth\u2013death process. This generalizes a result of Keilson and Ramaswamy by allowing birth and death rates to depend upon the size of the state space. We give sufficient conditions under which the convergence result of Keilson and Ramaswamy remains valid. The generalization allows us to apply our convergence result to examples from population biology: a Pearl\u2013Verhulst logistic population growth model and the susceptible-infective-susceptible (SIS) model for infectious spread. The limit distributions obtained suggest new finite-population approximations to the quasistationary distributions of these models, obtained by the method of cumulant closure. The new approximations are found to be both simple in form and accurate.<\/jats:p>","DOI":"10.1017\/s0021900200012869","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:29Z","timestamp":1459262969000},"page":"1036-1051","source":"Crossref","is-referenced-by-count":0,"title":["Approximating Quasistationary Distributions of Birth\u2013Death Processes"],"prefix":"10.1017","volume":"49","author":[{"given":"Damian","family":"Clancy","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S0021900200012869_ref19","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1011994180"},{"key":"S0021900200012869_ref20","doi-asserted-by":"publisher","DOI":"10.2307\/1427717"},{"key":"S0021900200012869_ref16","volume-title":"Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model","year":"2011"},{"key":"S0021900200012869_ref9","first-page":"685","volume":"27","year":"1989","journal-title":"J. Appl. Prob."},{"key":"S0021900200012869_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/S0040-5809(03)00074-1"},{"key":"S0021900200012869_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(84)90302-8"},{"key":"S0021900200012869_ref13","doi-asserted-by":"publisher","DOI":"10.1006\/jtbi.2001.2328"},{"key":"S0021900200012869_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988277"},{"key":"S0021900200012869_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/2533059"},{"key":"S0021900200012869_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/3212311"},{"key":"S0021900200012869_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(97)00050-1"},{"key":"S0021900200012869_ref5","first-page":"281","volume-title":"Proc. 5th Berkeley Symp. Math. Statist. Prob.","volume":"4","year":"1967"},{"key":"S0021900200012869_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988177"},{"key":"S0021900200012869_ref4","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1059060909"},{"key":"S0021900200012869_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-010-9177-8"},{"key":"S0021900200012869_ref2","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1294170510"},{"key":"S0021900200012869_ref1","doi-asserted-by":"publisher","DOI":"10.2307\/3214534"},{"key":"S0021900200012869_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(71)90087-3"},{"key":"S0021900200012869_ref18","doi-asserted-by":"publisher","DOI":"10.2307\/1427019"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200012869","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:17:41Z","timestamp":1682493461000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200012869\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":19,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["S0021900200012869"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200012869","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}