{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:52:38Z","timestamp":1759117958625,"version":"3.38.0"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:p>We study the <jats:italic>decay parameter<\/jats:italic> (the rate of convergence of the transition probabilities) of a birth-death process on {0, 1, \u2026}, which we allow to evanesce by escape, via state 0, to an absorbing state -1. Our main results are representations for the decay parameter under four different scenarios, derived from a unified perspective involving the orthogonal polynomials appearing in Karlin and McGregor's representation for the transition probabilities of a birth-death process, and the Courant-Fischer theorem on eigenvalues of a symmetric matrix. We also show how the representations readily yield some upper and lower bounds that have appeared in the literature.<\/jats:p>","DOI":"10.1017\/s0021900200012353","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:49:15Z","timestamp":1459248555000},"page":"278-289","source":"Crossref","is-referenced-by-count":2,"title":["Representations for the Decay Parameter of a Birth-Death Process Based on the Courant-Fischer Theorem"],"prefix":"10.1017","volume":"52","author":[{"given":"Erik A.","family":"van Doorn","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200012353_ref9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1957-0091566-1"},{"key":"S0021900200012353_ref10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1957-0094854-8"},{"volume-title":"An Introduction to Orthogonal Polynomials","year":"1978","key":"S0021900200012353_ref7"},{"key":"S0021900200012353_ref6","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1968.27.475"},{"key":"S0021900200012353_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-010-0068-7"},{"key":"S0021900200012353_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s11134-009-9134-9"},{"volume-title":"Eigenvalues, Inequalities, and Ergodic Theory","year":"2005","key":"S0021900200012353_ref4"},{"key":"S0021900200012353_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.01.032"},{"key":"S0021900200012353_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02898239"},{"key":"S0021900200012353_ref15","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1987.130.379"},{"key":"S0021900200012353_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02582989"},{"key":"S0021900200012353_ref14","doi-asserted-by":"publisher","DOI":"10.2307\/1427118"},{"key":"S0021900200012353_ref1","first-page":"173","volume":"26","year":"1974","journal-title":"Bull. Soc. Math. Belg."},{"key":"S0021900200012353_ref13","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1183667415"},{"key":"S0021900200012353_ref12","first-page":"319","volume":"5","year":"1999","journal-title":"Markov Process. Relat. Fields"},{"volume-title":"Matrix Analysis and Applied Linear Algebra","year":"2000","key":"S0021900200012353_ref11"},{"key":"S0021900200012353_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(82)90005-1"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200012353","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,4,22]],"date-time":"2017-04-22T15:48:29Z","timestamp":1492876109000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200012353\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3]]},"references-count":17,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["S0021900200012353"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200012353","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"type":"print","value":"0021-9002"},{"type":"electronic","value":"1475-6072"}],"subject":[],"published":{"date-parts":[[2015,3]]}}}