Fluctuations of interacting Markov chain Monte Carlo methods

被引：3

作者：

Bercu, Bernard ^{[2
,3
]}

Del Moral, Pierre ^{[2
,3
,4
]}

Doucet, Arnaud ^{[1
]}

机构：

[1] Univ Oxford, Dept Stat, Oxford OX1 3TG, England

[2] Univ Bordeaux, Ctr INRIA Bordeaux Sud Ouest, F-33405 Talence, France

[3] Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France

[4] Ctr Appl Math, F-9112 Palaiseau, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 04期

关键词：

Multivariate central limit theorems; Random fields; Martingale limit theorems; Self-interacting Markov chains; Markov chain Monte Carlo algorithms; ERGODICITY;

D O I：

10.1016/j.spa.2012.01.001

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：

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. (c) 2012 Elsevier By. All rights reserved.

引用

页码：1304 / 1331

页数：28

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