DEL MORAL, Pierre; PATRAS, Frédéric; RUBENTHALER, Sylvain

doi:10.1214/08-AAP565

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DEL MORAL, Pierre
University of New South Wales [Sydney] [UNSW]

PATRAS, Frédéric
Laboratoire Jean Alexandre Dieudonné [JAD]

RUBENTHALER, Sylvain
Laboratoire Jean Alexandre Dieudonné [JAD]

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The Annals of Applied Probability. 2009p. 778–825

Institute of Mathematical Statistics (IMS)

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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 $\mathbb{L}_p$-mean error bounds, and laws of large numbers for $U$-statistics.< Réduire

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combinatorial enumeration

tree

forest

Feynman-Kac semigroups

interacting particle systems

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Tree based functional expansions for Feynman--Kac particle models

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