BERCU, Bernard; DEL MORAL, Pierre; DOUCET, Arnaud

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BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]

DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]

DOUCET, Arnaud
Dept of Statistics & Dept of Computer Science
Department of Statistics [Vancouver] [UBC Statistics]

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Ce document a été publié dans

Stochastic Processes and their Applications. 2012, vol. 122, n° 4, p. 1304-1331

Elsevier

Résumé en anglais

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.< Réduire

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Institut de Mathématiques de Bordeaux (IMB) - UMR 5251