A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models

Bernard Bercu; Pierre Del Moral; Arnaud Doucet

A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models

Bernard Bercu ^{1, 2} Pierre Del Moral ^{1, 3, *} Arnaud Doucet ^{4, 5}

* Corresponding author

1 IMB - Institut de Mathématiques de Bordeaux

2 CQFD - Quality control and dynamic reliability

IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest

3 ALEA - Advanced Learning Evolutionary Algorithms

Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251

4 Dept of Statistics & Dept of Computer Science

5 Statistics - Department of Statistics

Abstract : We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original stochastic analysis based on semigroup techniques on distribution spaces and fluctuation theorems for self-interaction random fields. Besides the fluctuation analysis of these models, we also present a series of sharp $\LL_m$-mean error bounds in terms of the semigroup associated with the first order expansion of the limiting measure valued process, yielding what seems to be the first results of this type for this class of interacting processes. We illustrate these results in the context of Feynman-Kac integration semigroups arising in physics, biology and stochastic engineering science.

Keywords : and Feynman-Kac integrals Multivariate and functional central limit theorems random fields martingale limit theorems self-interacting Markov chains Markov chain Monte Carlo models and Feynman-Kac integrals.

Document type :

Journal articles

Domain :

Mathematics [math] / Probability [math.PR]

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https://hal.inria.fr/inria-00227534
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