Variances of first passage times in a Markov chain with applications to mixing times
| dc.contributor.author | Hunter, J.J. | |
| dc.date.accessioned | 2013-05-20T04:08:27Z | |
| dc.date.available | 2013-05-20T04:08:27Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | In an earlier paper the author introduced the statisticηi j ijπ j m = m = Σ 1 as a measure of the “mixing time” or “time to stationarity” in a finite irreducible discrete time Markov chain with stationary distribution {pj} and mij 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 ηi = 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 vi , starting in state i. The vi , 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 mixing times, mij (2) , and the variance of the first passage times, in a discrete time Markov chain is carried out leading to some new results. | en |
| dc.identifier.citation | Hunter, J.J. (2006), Variances of first passage times in a Markov chain with applications to mixing times, Research Letters in the Information and Mathematical Sciences, 10, 17-48 | en |
| dc.identifier.issn | 1175-2777 | |
| dc.identifier.uri | http://hdl.handle.net/10179/4484 | |
| dc.language.iso | en | en |
| dc.publisher | Massey University | en |
| dc.subject | First passage time | en |
| dc.subject | Markov chains | en |
| dc.title | Variances of first passage times in a Markov chain with applications to mixing times | en |
| dc.type | Article | en |
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