The distribution of Mixing Times in Markov Chains

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aut.relation.issue1
aut.relation.volume30
aut.researcherHunter, Jeffrey Joseph
dc.contributor.authorHunter, JJ
dc.date.accessioned2012-12-04T02:08:56Z
dc.date.available2012-12-04T02:08:56Z
dc.date.copyright2012
dc.date.issued2012
dc.description.abstractThe distribution of the “mixing time” or the “time to stationarity” in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the mixing time, starting in state i, are derived and special cases explored. This extends the results of the author regarding the expected time to mixing [Hunter, J J (2006). Mixing times with applications to perturbed Markov chains. Linear Algebra and its Applications, 417, 108-123] and the variance of the times to mixing, [Hunter, J J (2008). Variances of First Passage Times in a Markov chain with applications to Mixing Times. Linear Algebra and its Applications, 429, 1135-1162]. Some new results for the distribution of the recurrence and the first passage times in a general irreducible three-state Markov chain are also presented.
dc.identifier.citationAsia - Pacific Journal of Operational Research, vol.30(1)
dc.identifier.doi10.1142/S0217595912500455
dc.identifier.issn1793-7019
dc.identifier.urihttps://hdl.handle.net/10292/4810
dc.languageEnglish
dc.publisherWorld Scientific Publishing Co & Operational Research Society of Singapore
dc.relation.isreplacedby10292/4979
dc.relation.isreplacedbyhttp://hdl.handle.net/10292/4979
dc.relation.urihttp://dx.doi.org/10.1142/S0217595912500455
dc.rightsElectronic version of an article published as (please see citation) [Article DOI] © copyright World Scientific Publishing Company (please see Publisher’s Version).
dc.rights.accessrightsOpenAccess
dc.subjectMarkov chains
dc.subjectStationary distribution
dc.subjectFrst passage times
dc.subjectHitting times
dc.subjectMixing times
dc.subjectTime to stationarity
dc.subjectKemeny constant
dc.subjectDistributions
dc.titleThe distribution of Mixing Times in Markov Chains
dc.typeJournal Article
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