A Berry.Esseen theorem for Feynman.Kac and interacting particle models

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman.Kac particle approximation models. We design an original approach based on new Berry.Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical theory and apply to a class of branching and genealogical path-particle models arising in nonlinear filtering literature as well as in statistical physics and biology.