Berry-Esseen Type bound of a sequence {XNYN} and its application

Using the recent results obtained by combining Malliavin calculus and Stein's method, we obtain the Berry-Esseen type bound of a sequence of the random variables of the form {XNYN,N∈N}, where XN and YN are square integrable random variables such that their Malliavin derivatives also are square integrable. The aim of this paper is to develop the new techniques, allowing us to obtain sharp Berry-Esseen bound. As an application, we will discuss the rate of convergence of the distribution of the maximum likelihood estimator of a parameter appearing in a stochastic partial differential equation.