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

• 成果类型: Article
• 署名作者: Del Moral, P; Tindel, S
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite de Lorraine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000792
• 发表日期: 2005
• 页码: 941-962
• 关键词: CENTRAL-LIMIT-THEOREM; systems

摘要

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.