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
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
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.
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Bernard Bercu, Pierre del Moral, Arnaud Doucet. A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2009, 14 (73), pp.2130-2155. ⟨inria-00227534v5⟩

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