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Variances of first passage times in a Markov chain with applications to mixing times by Jeffrey J. Hunter is a Mathematics article available to read on EtoBox.

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In an earlier paper [J.J. Hunter, Mixing times with applications to perturbed Markov chains, Linear Algebra Appl. 417 (2006) 108-123] the author introduced the statistic η i = m j =1 m ij π j as a measure of the "mixing time" or "time to stationarity" in a finite irreducible discrete time Markov chain with stationary distribution {π j } and m ij as the mean first passage time from state i to state j of the Markov chain. This was shown to be independent of the initial state i with η i = η for all i, minimal in the case of a periodic chain, yet can be arbitrarily large in a variety of situations. In this paper we explore the variance of the mixing time v i , starting in state i. The v i are shown to depend on i and an exploration of recommended starting states, given knowledge of the transition probabilities, is considered. As a preamble, a study of the computation of second moments of the first passage times, m (2) ij , and the variance of the first passage times, in a discrete time Markov chain is carried out leading to some new results.

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Author

Jeffrey J. Hunter

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0024-3795)

Published

2008

Language

EN

Field

Mathematics (Physical Sciences)