Renewal theory and computable convergence rates for geometrically ergodic Markov chains

Details Renewal theory and computable convergence rates for geometrically ergodic Markov chains Renewal theory and computable convergence rates for geometrically ergodic Markov chains

2005-03-24

arxiv.org/abs/math/0503515v1

Annals of Applied Probability 2005, Vol. 15, No. 1B, 700-738

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000710 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000710

We 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.

Affiliated with

Also associated with

No associations

Rating

Renewal theory and computable convergence rates for geometrically ergodic Markov chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Renewal theory and computable convergence rates for geometrically ergodic Markov chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Renewal theory and computable convergence rates for geometrically ergodic Markov chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586875