Convergence of U-statistics for interacting particle systems
Probability
2010-02-02 v1 Statistics Theory
Statistics Theory
Abstract
The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the corresponding algorithms, the distributions of the particles are correlated -although any finite number of them is asymptotically independent with respect to the total number N of particles. In the present article, exploiting the fine asymptotics of particle systems, we prove convergence theorems for U-statistics in this framework.
Cite
@article{arxiv.1002.0224,
title = {Convergence of U-statistics for interacting particle systems},
author = {P. Del Moral and F. Patras and S. Rubenthaler},
journal= {arXiv preprint arXiv:1002.0224},
year = {2010}
}