{"title":"离散Markov链的吸收概率和平均吸收时间","authors":"N. Halidias","doi":"10.1515/MCMA-2021-2084","DOIUrl":null,"url":null,"abstract":"Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. 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 A before reach B generalizing this result for a sequence of sets A1,A2,…,Ak{A_{1},A_{2},\\dots,A_{k}}.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"27 1","pages":"105 - 115"},"PeriodicalIF":0.8000,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/MCMA-2021-2084","citationCount":"0","resultStr":"{\"title\":\"On the absorption probabilities and mean time for absorption for discrete Markov chains\",\"authors\":\"N. Halidias\",\"doi\":\"10.1515/MCMA-2021-2084\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. 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 A before reach B generalizing this result for a sequence of sets A1,A2,…,Ak{A_{1},A_{2},\\\\dots,A_{k}}.\",\"PeriodicalId\":46576,\"journal\":{\"name\":\"Monte Carlo Methods and Applications\",\"volume\":\"27 1\",\"pages\":\"105 - 115\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-02-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/MCMA-2021-2084\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Monte Carlo Methods and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/MCMA-2021-2084\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monte Carlo Methods and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/MCMA-2021-2084","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
On the absorption probabilities and mean time for absorption for discrete Markov chains
Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. 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 A before reach B generalizing this result for a sequence of sets A1,A2,…,Ak{A_{1},A_{2},\dots,A_{k}}.
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