Renewal theory and computable convergence rates for geometrically ergodic Markov chains

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dc.creatorBaxendale, Peter H.
dc.date2005-03-24
dc.date.accessioned2026-07-07T05:18:18Z
dc.date.available2026-07-07T05:18:18Z
dc.descriptionWe give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and Tweedie, and from estimates using coupling, although we start from essentially the same assumptions of a drift condition toward a ``small set.'' The estimates show a noticeable improvement on existing results if the Markov chain is reversible with respect to its stationary distribution, and especially so if the chain is also positive. The method of proof uses the first-entrance-last-exit decomposition, together with new quantitative versions of a result of Kendall from discrete renewal theory.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051604000000710 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503515
dc.identifierhttp://arxiv.org/abs/math/0503515
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 1B, 700-738
dc.identifierdoi:10.1214/105051604000000710
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74615
dc.subjectProbability
dc.subject60J27 (Primary) 60K05, 65C05. (Secondary)
dc.titleRenewal theory and computable convergence rates for geometrically ergodic Markov chains
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