A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals

TL;DR

This paper establishes a new explicit bound on the total variation distance for sums of Wiener chaos variables and applies it to Gaussian approximations of ratios of stochastic integrals.

Contribution

It introduces a novel explicit bound on the total variation distance for finite Wiener chaos sums and applies it to Gaussian approximations of ratios of stochastic integrals.

Findings

New explicit bound on total variation distance

Upper bound for Kolmogorov distance between ratios of stochastic integrals and Gaussian

Enhanced understanding of Gaussian approximations in Wiener chaos

Abstract

In this paper we provide a new explicit bound on the total variation distance between a standardized partial sum of random variables belonging to a finite sum of Wiener chaoses and a standard normal random variable. We apply our result to derive an upper bound for the Kolmogorov distance between a ratio of multiple stochastic integrals and a Gaussian random variable.