Quantitative bounds on convergence of time-inhomogeneous Markov chains
Quantitative bounds on convergence of time-inhomogeneous Markov chains
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DOI：
10.1214/105051604000000620
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发表时间：
2004-11
影响因子：
1.8
通讯作者：
R. Douc;Eric Moulines;J. Rosenthal
中科院分区：
文献类型：
--
作者：
R. Douc;Eric Moulines;J. Rosenthal
马尔可夫链的收敛速度是近年来研究的热点问题。特别地，Meyn和Tweedie [Ann. Appl. Probab. 4（1994）981-1101]，Rosenthal [J. Amer. Statistist. Assoc.90（1995）558-566]，Roberts和Tweedie [Stochastic Process. 80（1999）211-229]、Jones和Hobert [Statist. Sci. 16（2001）312-334]和Fort [Ph.D.论文（2001）巴黎大学第六届]。本文推广了Rosenthal [J. Amer. Statistist. Assoc.90（1995）558-566]，其涉及时间齐次马尔可夫链的定量收敛速率。我们的扩展允许我们考虑f-全变差距离（而不是全变差）和时间非齐次马尔可夫链。我们将我们的结果应用于模拟退火。
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.