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November 2004 Quantitative bounds on convergence of time-inhomogeneous Markov chains
R. Douc, E. Moulines, Jeffrey S. Rosenthal
Ann. Appl. Probab. 14(4): 1643-1665 (November 2004). DOI: 10.1214/105051604000000620

Abstract

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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R. Douc. E. Moulines. Jeffrey S. Rosenthal. "Quantitative bounds on convergence of time-inhomogeneous Markov chains." Ann. Appl. Probab. 14 (4) 1643 - 1665, November 2004. https://doi.org/10.1214/105051604000000620

Information

Published: November 2004
First available in Project Euclid: 5 November 2004

zbMATH: 1072.60059
MathSciNet: MR2099647
Digital Object Identifier: 10.1214/105051604000000620

Subjects:
Primary: 60J22 , 60J27

Keywords: convergence rate , coupling , f-total variation , Markov chain Monte Carlo , simulated annealing

Rights: Copyright © 2004 Institute of Mathematical Statistics

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