Total variation distance between two double Wiener-Itô integrals

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.