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-Itô 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.
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