Fluctuations of interacting Markov chain Monte Carlo methods

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• 作者：Bernard Bercu^a ; ^{Bernard.Bercu@math.u-bordeaux1.fr} ; Pierre Del Moral^a ; ^b ; ^{Pierre.Del-Moral@inria.fr} ; Arnaud Doucet^c ; ^{Doucet@stats.ox.ac.uk}
• 关键词：primary ; 47H20 ; 60G35 ; 60J85 ; 62G09 ; secondary ; 47D08 ; 47G10 ; 62L20
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：April, 2012
• 卷：122
• 期：4
• 页码：1304-1331
• 文件大小：298 K

摘要

We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the class of nonlinear Markov chains interacting with their empirical occupation measures. We develop an original theoretical analysis based on resolvent operators and semigroup techniques to analyze the fluctuations of their occupation measures around their limiting values.