Tree based functional expansions for Feynman-Kac particle models

Pierre Del Moral 1 Frédéric Patras 2 Sylvain Rubenthaler 2
1 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : 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 Lp-mean error bounds, and laws of large numbers for U-statistics.
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Contributor : Sylvain Rubenthaler <>
Submitted on : Wednesday, June 22, 2011 - 10:42:23 AM
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Pierre Del Moral, Frédéric Patras, Sylvain Rubenthaler. Tree based functional expansions for Feynman-Kac particle models. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2009, 19 (2), pp.778-825. ⟨10.1214/08-AAP565⟩. ⟨hal-00602363⟩



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