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Variances of first passage times in a Markov chain with applications to mixing times
- Source :
-
Linear Algebra & its Applications . Sep2008, Vol. 429 Issue 5/6, p1135-1162. 28p. - Publication Year :
- 2008
-
Abstract
- Abstract: 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 as a measure of the “mixing time” or “time to stationarity” in a finite irreducible discrete time Markov chain with stationary distribution and 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 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 , starting in state i. The 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, , and the variance of the first passage times, in a discrete time Markov chain is carried out leading to some new results. [Copyright &y& Elsevier]
- Subjects :
- *VARIANCES
*MARKOV processes
*LINEAR algebra
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 429
- Issue :
- 5/6
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 33138529
- Full Text :
- https://doi.org/10.1016/j.laa.2007.06.016