Ciprian Tudor
University of Lille, Lille, France

Let $ (X_{1}, X_{2}, \ldots, X_{n})$ be a random vector and denote by $ P_{ (X_{1},X_{2},\ldots, X_{n})}$ its probability distribution on $\mathbb{R} ^{n}$. We develop a multidimensional Stein-Malliavin calculus which allows to measure the Wasserstein distance between the law $ P_{ (X_{1},X_{2},..., X_{n})}$ and the probability distribution $ P_{Z}\otimes P_{ (X_{2},..., X_{n})}$, where $Z$ is a Gaussian random variable. We also regard the particular case of random vectors in Wiener chaos and we give an asymptotic version of this result. As an example, we derive the rate of convergence for the Wasserstein distance for a two-dimensional sequence of multiple stochastic integrals, the first converging to a normal law and the second to a Rosenblatt distribution.