Tree based functional expansions for Feynman--Kac particle models

Details Tree based functional expansions for Feynman--Kac particle models Tree based functional expansions for Feynman--Kac particle models

2009-06-23

arxiv.org/abs/0906.4249v1

Annals of Applied Probability 2009, Vol. 19, No. 2, 778-825

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP565 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP565

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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