Total variation distance between stochastic polynomials and invariance principles
Probability
2019-12-03 v1
Abstract
The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence one obtains an invariance principle for such polynomials. This generalizes known results concerning the total variation distance between two multiple stochastic integrals on one hand, and invariance principles in Kolmogorov distance for multi-linear stochastic polynomials on the other hand. As an application we first discuss the asymptotic behavior of U-statistics associated to polynomial kernels. Moreover we also give an example of CLT associated to quadratic forms.
Keywords
Cite
@article{arxiv.1705.05194,
title = {Total variation distance between stochastic polynomials and invariance principles},
author = {Vlad Bally and Lucia Caramellino},
journal= {arXiv preprint arXiv:1705.05194},
year = {2019}
}