Quantitative bounds on convergence of time-inhomogeneous Markov chains

• 成果类型: Article
• 署名作者: Douc, R; Moulines, E; Rosenthal, JS
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; IMT - Institut Mines-Telecom; IMT Atlantique; Centre National de la Recherche Scientifique (CNRS); University of Toronto
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000620
• 发表日期: 2004
• 页码: 1643-1665
• 关键词: rates

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.