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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


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.


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

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

Primary: 60J22 , 60J27

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

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 4 • November 2004
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