Total variation distance between two double Wiener-It\^o integrals

TL;DR

This paper improves the rate of convergence bounds for the total variation distance between two double Wiener-Itô integrals and applies these results to analyze the convergence of a fractional Brownian motion functional to a Rosenblatt distribution.

Contribution

It introduces an improved inequality for the total variation distance between double Wiener-Itô integrals using recent methods, enhancing previous bounds.

Findings

Enhanced convergence rate bounds for double Wiener-Itô integrals.

Application to fractional Brownian motion functionals converging to Rosenblatt distribution.

Quantitative analysis of convergence in stochastic processes.

Abstract

Using an approach recently developed by Nourdin and Poly, we improve the rate in an inequality for the total variation distance between two double Wiener-It\^o integrals originally due to Davydov and Martynova. An application to the rate of convergence of a functional of a correlated two-dimensional fractional Brownian motion towards the Rosenblatt random variable is then given, following a previous study by Maejima and Tudor.