The Annals of Applied Probability

Quantitative bounds on convergence of time-inhomogeneous Markov chains

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

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 5 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1099674073

Digital Object Identifier
doi:10.1214/105051604000000620

Mathematical Reviews number (MathSciNet)
MR2099647

Zentralblatt MATH identifier
1072.60059

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1099674073


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