Coalescent tree based functional representations for some Feynman-Kac particle models
Probability
2016-08-16 v1
Abstract
We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original combinatorial, and permutation group analysis of a special class of forests. They provide refined non asymptotic propagation of chaos type properties, as well as sharp -mean error bounds, and laws of large numbers for -statistics. Applications to particle interpretations of the top eigenvalues, and the ground states of Schr\"{o}dinger semigroups are also discussed.
Keywords
Cite
@article{arxiv.math/0607453,
title = {Coalescent tree based functional representations for some Feynman-Kac particle models},
author = {Pierre Del Moral and Frédéric Patras and Sylvain Rubenthaler},
journal= {arXiv preprint arXiv:math/0607453},
year = {2016}
}