The Annals of Applied Probability

Tree based functional expansions for Feynman–Kac particle models

Pierre Del Moral, Frédéric Patras, and Sylvain Rubenthaler

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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.

Article information

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

Dates
First available in Project Euclid: 7 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1241702250

Digital Object Identifier
doi:10.1214/08-AAP565

Mathematical Reviews number (MathSciNet)
MR2521888

Zentralblatt MATH identifier
1189.60171

Subjects
Primary: 47D08: Schrödinger and Feynman-Kac semigroups 60C05: Combinatorial probability 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 65C35: Stochastic particle methods [See also 82C80]
Secondary: 31B10: Integral representations, integral operators, integral equations methods 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 65C05: Monte Carlo methods 92D25: Population dynamics (general)

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

Citation

Del Moral, Pierre; Patras, Frédéric; Rubenthaler, Sylvain. Tree based functional expansions for Feynman–Kac particle models. Ann. Appl. Probab. 19 (2009), no. 2, 778--825. doi:10.1214/08-AAP565. https://projecteuclid.org/euclid.aoap/1241702250


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References

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