Xiaochuan Yang (University of Luxembourg), February 21, 2019
Abstract: The Breuer-Major theorem provides sufficient conditions in order that a normalized sum of non-linear functionals of Gaussian random fields exhibits Gaussian fluctuation. Such a result has far-reaching applications in statistical inference of Gaussian models. In this talk, I will be focusing on the rate of convergence in the total variation distance of the Breuer-Major theorem. To this end, we apply Malliavin calculus (stochastic calculus of variation) techniques, Stein’s method for normal approximations, and Gebelein’s inequality for functionals of correlated Gaussian fields. Based on joint work with I. Nourdin and G. Peccati.