{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T01:00:45Z","timestamp":1649120445371},"reference-count":4,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this note we study the probability and the\nmean time for absorption for discrete time Markov chains. In particular, we are\ninterested in estimating the mean time for absorption when\nabsorption is not certain and connect it with some other known\nresults. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set <jats:italic>A<\/jats:italic> before reach <jats:italic>B<\/jats:italic> generalizing this result for a sequence of sets <jats:inline-formula id=\"j_mcma-2021-2084_ineq_9999_w2aab3b7d434b1b6b1aab1c14b1b5Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>A<\/m:mi>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:msub>\n                              <m:mo>,<\/m:mo>\n                              <m:msub>\n                                 <m:mi>A<\/m:mi>\n                                 <m:mn>2<\/m:mn>\n                              <\/m:msub>\n                              <m:mo>,<\/m:mo>\n                              <m:mi mathvariant=\"normal\">\u2026<\/m:mi>\n                              <m:mo>,<\/m:mo>\n                              <m:msub>\n                                 <m:mi>A<\/m:mi>\n                                 <m:mi>k<\/m:mi>\n                              <\/m:msub>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2021-2084_eq_0172.png\" \/>\n                        <jats:tex-math>{A_{1},A_{2},\\dots,A_{k}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.<\/jats:p>","DOI":"10.1515\/mcma-2021-2084","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T22:32:47Z","timestamp":1613169167000},"page":"105-115","source":"Crossref","is-referenced-by-count":0,"title":["On the absorption probabilities and mean time for absorption for discrete Markov chains"],"prefix":"10.1515","volume":"27","author":[{"given":"Nikolaos","family":"Halidias","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial-Financial Mathematics , University of the Aegean , Karlovassi 83200 Samos , Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2021,2,2]]},"reference":[{"key":"2021053122091977356_j_mcma-2021-2084_ref_001_w2aab3b7d434b1b6b1ab2ab1Aa","unstructured":"J.  Kemeny and J.  Snell,\nFinite Markov Chains,\nSpringer, Berlin, 1974."},{"key":"2021053122091977356_j_mcma-2021-2084_ref_002_w2aab3b7d434b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"T.  Sheskin,\nConditional mean first passage time in a Markov chain,\nInt. J. Manag. Sci. Eng. Manag. 8 (2013), 32\u201337.","DOI":"10.1080\/17509653.2013.783187"},{"key":"2021053122091977356_j_mcma-2021-2084_ref_003_w2aab3b7d434b1b6b1ab2ab3Aa","unstructured":"Y.  Suhov and  Mark Kelbert,\nMarkov Chains: A Primer in Random Processes and Their Applications,\nCambridge University, Cambridge, 2008."},{"key":"2021053122091977356_j_mcma-2021-2084_ref_004_w2aab3b7d434b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"D.  Walker,\nThe expected time until absorption when absorption is not certain,\nJ. Appl. Probab. 35 (1998), 812\u2013823.","DOI":"10.1017\/S0021900200016521"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2021-2084\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2021-2084\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T01:20:41Z","timestamp":1622510441000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2021-2084\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,2]]},"references-count":4,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2,2]]},"published-print":{"date-parts":[[2021,6,1]]}},"alternative-id":["10.1515\/mcma-2021-2084"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2021-2084","relation":{},"ISSN":["1569-3961","0929-9629"],"issn-type":[{"value":"1569-3961","type":"electronic"},{"value":"0929-9629","type":"print"}],"subject":[],"published":{"date-parts":[[2021,2,2]]}}}