• Login
    View Item 
    •   Home
    • Massey University Departments
    • Institute of Natural and Mathematical Sciences
    • Research Letters in the Information and Mathematical Sciences
    • View Item
    •   Home
    • Massey University Departments
    • Institute of Natural and Mathematical Sciences
    • Research Letters in the Information and Mathematical Sciences
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Variances of first passage times in a Markov chain with applications to mixing times

    Icon
    View/Open Full Text
    Variances_of_first_passage_times_in_a_Markov_chain_with_applications_to_mixing_times.pdf (1.166Mb)
    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.
    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
    Date
    2006
    Author
    Hunter, J.J.
    Publisher
    Massey University
    URI
    http://hdl.handle.net/10179/4484
    Collections
    • Research Letters in the Information and Mathematical Sciences
    Metadata
    Show full item record

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1
     

     

    Tweets by @Massey_Research
    Information PagesContent PolicyDepositing content to MROCopyright and Access InformationDeposit LicenseDeposit License SummaryTheses FAQFile FormatsDoctoral Thesis Deposit

    Browse

    All of MROCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister

    Statistics

    View Usage Statistics

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1