Estimation of Wiener--Ito integrals and polynomials of independent Gaussian random variables
Abstract
In this paper I prove good estimates on the moments and tail distribution of -fold Wiener--It\^o integrals and also present their natural counterpart for polynomials of independent Gaussian random variables. The proof is based on the so-called diagram formula for Wiener--It\^o integrals which yields a good representation for their products as a sum of such integrals. I intend to show in a subsequent paper that this method also yields good estimates for degenerate -statistics. The main result of this paper is a generalization of the estimates of Hanson and Wright about bilinear forms of independent standard normal random variables. On the other hand, it is a weaker estimate than the main result of a paper of Lata{\l}a [6]. But that paper contains an error, and it is not clear whether its result is true. This question is also discussed here.
Keywords
Cite
@article{arxiv.0803.1453,
title = {Estimation of Wiener--Ito integrals and polynomials of independent Gaussian random variables},
author = {Peter Major},
journal= {arXiv preprint arXiv:0803.1453},
year = {2008}
}