{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:41:16Z","timestamp":1682494876460},"reference-count":15,"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>We are interested in continuous-time, denumerable state controlled Markov chains (CMCs), with compact Borel action sets, and possibly unbounded transition and reward rates, under the discounted reward optimality criterion. For such CMCs, we propose a definition of a sequence of control models {\u2133<jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub>} converging to a given control model \u2133, which ensures that the discount optimal reward and policies of \u2133<jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> converge to those of \u2133. As an application, we propose a finite-state and finite-action truncation technique of the original control model \u2133, which is illustrated by approximating numerically the optimal reward and policy of a controlled population system with catastrophes. We study the corresponding convergence rates.<\/jats:p>","DOI":"10.1017\/s0021900200012882","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:29Z","timestamp":1459262969000},"page":"1072-1090","source":"Crossref","is-referenced-by-count":0,"title":["Discounted Continuous-Time Controlled Markov Chains: Convergence of Control Models"],"prefix":"10.1017","volume":"49","author":[{"given":"Tom\u00e1s","family":"Prieto-Rumeau","sequence":"first","affiliation":[]},{"given":"On\u00e9simo","family":"Hern\u00e1ndez-Lerma","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S0021900200012882_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.09.013"},{"key":"S0021900200012882_ref10","first-page":"84","volume-title":"Modern Trends in Controlled Stochastic Processes","year":"2010"},{"key":"S0021900200012882_ref8","doi-asserted-by":"publisher","DOI":"10.1287\/moor.6.4.493"},{"key":"S0021900200012882_ref7","volume-title":"Numerical Methods for Stochastic Control Problems in Continuous Time","year":"2001"},{"key":"S0021900200012882_ref6","volume-title":"Adaptive Markov Control Processes","year":"1989"},{"key":"S0021900200012882_ref5","volume-title":"Continuous-Time Markov Decision Processes","year":"2009"},{"key":"S0021900200012882_ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2002.808469"},{"key":"S0021900200012882_ref3","doi-asserted-by":"publisher","DOI":"10.1023\/B:ACAP.0000003675.06200.45"},{"key":"S0021900200012882_ref15","doi-asserted-by":"publisher","DOI":"10.1287\/moor.3.3.231"},{"key":"S0021900200012882_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s001860200209"},{"key":"S0021900200012882_ref14","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997280294"},{"key":"S0021900200012882_ref1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.19.1.169"},{"key":"S0021900200012882_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.07.014"},{"key":"S0021900200012882_ref12","volume-title":"Principles of Mathematical Analysis","year":"1976"},{"key":"S0021900200012882_ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2009.2033848"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200012882","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:18:06Z","timestamp":1682493486000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200012882\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":15,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["S0021900200012882"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200012882","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}