The Annals of Applied Probability

Quantitative bounds on convergence of time-inhomogeneous Markov chains

R. Douc, E. Moulines, and Jeffrey S. Rosenthal

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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.

Article information

Ann. Appl. Probab., Volume 14, Number 4 (2004), 1643-1665.

First available in Project Euclid: 5 November 2004

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Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60J22: Computational methods in Markov chains [See also 65C40]

Convergence rate coupling Markov chain Monte Carlo simulated annealing f-total variation


Douc, R.; Moulines, E.; Rosenthal, Jeffrey S. Quantitative bounds on convergence of time-inhomogeneous Markov chains. Ann. Appl. Probab. 14 (2004), no. 4, 1643--1665. doi:10.1214/105051604000000620.

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