Quantitative bounds on convergence of time-inhomogeneous Markov chains

Details Quantitative bounds on convergence of time-inhomogeneous Markov chains Quantitative bounds on convergence of time-inhomogeneous Markov chains

2005-03-24

arxiv.org/abs/math/0503532v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 1643-1665

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000620 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000620

Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994) 981-1101], Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566], Roberts and Tweedie [Stochastic Process. Appl. 80 (1999) 211-229], Jones and Hobert [Statist. Sci. 16 (2001) 312-334] and Fort [Ph.D. thesis (2001) Univ. Paris VI]. In this paper, we extend a result of Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566] that concerns quantitative convergence rates for time-homogeneous Markov chains. Our extension allows us to consider f-total variation distance (instead of total variation) and time-inhomogeneous Markov chains. We apply our results to simulated annealing.

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