Abstract. The purpose of this paper is to establish the multivariate normal convergence for the average of certain Volterra processes constructed from a fractional Brownian motion with Hurst parameter H > . Some applications to parameter estimation are then discussed.

Using an approach recently developed by Nourdin and Poly [5], we improve the rate in an inequality for the total variation distance between two double Wiener-Itô integrals originally due to Davydov and Martynova [2]. 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 [3].

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