A Functional Central Limit Theorem for a Class of Interacting Markov
Chain Monte Carlo Methods
Bernard Bercu, INRIA et Institut de Mathématiques de Bordeaux
Pierre Del Moral, INRIA et Institut de Mathématiques de Bordeaux
Arnaud Doucet, University of
British Columbia
Abstract
We present a functional central limit theorem for a new class of interacting
Markov chain Monte Carlo algorithms. These stochastic algorithms have been
recently introduced to solve non-linear measure-valued equations. We provide
an original theoretical analysis based on semigroup techniques on
distribution spaces and fluctuation theorems for self-interacting random
fields. Additionally we also present a series of sharp mean error bounds in
terms of the semigroup associated with the first order expansion of the
limiting measure-valued process. We illustrate our results in the context of
Feynman-Kac semigroups
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