On the absorption probabilities and mean time for absorption for discrete Markov chains

Halidias Nikolaos ()
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Halidias Nikolaos: Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi83200 Samos, Greece

Monte Carlo Methods and Applications, 2021, vol. 27, issue 2, 105-115

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}}.

Keywords: Discrete Markov chains; absorption probabilities; mean time to absorption; probability generating functions (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/mcma-2021-2084

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