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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,uctuation theorems for self- interaction random,elds. Besides the uctuation analysis of these models, we also present a series of sharp Lp-mean error bounds in terms of the semigroup associated with the rst order expansion of the limiting measure valued process, yielding what seems to be the,rst 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. Key-words: Multivariate and functional central limit theorems, random

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