Probability Seminar "Stein’s method and asymptotic independence" November 6, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)
Local: Google Meet
Speaker: Ciprian Tudor (Université de Lille)
Abstract: If Y is a random vector in R^d we denote by P_Y its probability distribution. Consider a random variable X and a d-dimensional random vector Y. We develop a multidimensional variant of the Stein-Malliavin calculus which allows to measure the Wasserstein distance between the law P_(X, Y) and the probability distribution P_Z x P_Y, where Z is a Gaussian random variable. That is, we give estimates, in terms of the Malliavin operators, for the distance between the law of the random vector (X, Y) and the law of the vector (Z,Y), where Z is Gaussian and independent of Y.
Then we focus on the particular case of random vectors in Wiener chaos and we give an asymptotic version of this result. In this situation, this variant of the Stein-Malliavin calculus has strong and unexpected consequences.
More complete information about the seminars can be found at DME.