Tree based functional expansions for Feynman--Kac particle models
Language
en
Article de revue
This item was published in
The Annals of Applied Probability. 2009p. 778–825
Institute of Mathematical Statistics (IMS)
English 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 ...Read more >
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.Read less <
English Keywords
combinatorial enumeration
tree
forest
Feynman-Kac semigroups
interacting particle systems
Origin
Hal imported