TREE BASED FUNCTIONAL EXPANSIONS FOR FEYNMAN-KAC PARTICLE MODELS

• 成果类型: Article
• 署名作者: Del Moral, Pierre; Patras, Frederic; Rubenthaler, Sylvain
• 署名单位: Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP565
• 发表日期: 2009
• 页码: 778-825
• 关键词: RENORMALIZATION

摘要

We design exact polynomial expansions of a class of Feynman-Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any order is related naturally to the number of coalescences of the trees. Our results include an extension of the Wick product formula to interacting particle systems. They also provide refined nonasymptotic propagation of chaos-type properties, as well as sharp L-p-mean error bounds, and laws of large numbers for U-statistics.