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

Details A Berry-Esseen theorem for Feynman-Kac and interacting particle models A Berry-Esseen theorem for Feynman-Kac and interacting particle models

2005-03-24

arxiv.org/abs/math/0503522v1

Annals of Applied Probability 2005, Vol. 15, No. 1B, 941-962

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000792 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000792

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.

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