Tree based functional expansions for Feynman–Kac particle models

Tree based functional expansions for Feynman–Kac particle models

Pierre Del Moral, Frédéric Patras, and Sylvain Rubenthaler

Source: Ann. Appl. Probab. Volume 19, Number 2 (2009), 778-825.

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

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Primary Subjects: 47D08, 60C05, 60K35, 65C35

Secondary Subjects: 31B10, 60J80, 65C05, 92D25

Keywords: Feynman–Kac semigroups; interacting particle systems; trees and forests; automorphism groups; combinatorial enumeration

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoap/1241702250
Digital Object Identifier: doi:10.1214/08-AAP565
Mathematical Reviews number (MathSciNet): MR2521888
Zentralblatt MATH identifier: 1189.60171

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