Fluctuations 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 general class of interacting Markov chain Monte Carlo interpretations of discrete generation measure-valued equations. The path space models associated with these stochastic processes 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 fluctuation of their occupation measures around their limiting value. We also present a set of simple regularity conditions that applies to interacting Markov chain Monte Carlo models on path spaces, yielding what seems to be the first fluctuation theorems for this class of self-interacting models.
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Bernard Bercu, Pierre del Moral, Arnaud Doucet. Fluctuations of Interacting Markov Chain Monte Carlo Models. Stochastic Processes and their Applications, Elsevier, 2012, 122 (4), pp.1304-1331. ⟨inria-00227536v5⟩

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