Research Letters in the Information and Mathematical Sciences

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Research Letters welcomes papers from staff and graduate students at Massey University in the areas of: Computer Science, Information Science, Mathematics, Statistics and the Physical and Engineering Sciences. Research letters is a preprint series that accepts articles of completed research work, technical reports, or preliminary results from ongoing research. After editing, articles are published online and can be referenced, or handed out at conferences. Copyright remains with the authors and the articles can be used as preprints to academic journal publications or handed out at conferences. Editors Dr Elena Calude Dr Napoleon Reyes The guidelines for writing a manuscript can be accessed here.

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Author: search.filters.author.Hunter, J.J.Subject: search.filters.subject.Markov chains

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    Variances of first passage times in a Markov chain with applications to mixing times
    (Massey University, 2006) Hunter, J.J.
    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.