Quantitative bounds on convergence of time-inhomogeneous Markov chains

被引：68

作者：

Douc, R

Moulines, E

Rosenthal, JS

机构：

[1] Ecole Polytech, CMAP, F-91128 Palaiseau, France

[2] Ecole Natl Super Telecommun Bretagne, Dept TSI, CNRS, URA 820, F-75634 Paris 13, France

[3] Univ Toronto, Dept Stat, Toronto, ON M5S 3G3, Canada

来源：

ANNALS OF APPLIED PROBABILITY | 2004年 / 14卷 / 04期

关键词：

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

D O I：

10.1214/105051604000000620

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：1643 / 1665

页数：23

共 20 条

[1] Convergence of simulated annealing using Foster-Lyapunov criteria [J].