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

**Bernard Bercu**

*(Université de Bordeaux)*

**Pierre Del Moral**

*(INRIA et Université 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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Pages: 2130-2155

Publication Date: October 4, 2009

DOI: 10.1214/EJP.v14-701

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