Speaker: Xiaoqin Guo, University of Cincinati.

Title: On the rate of convergence of the martingale central limit theorem in Wasserstein distances. 

Abstract: We consider the rate of convergence of the central limit theorem (CLT) for martingales. For martingales with a wide range of integrability, we will quantify the rate of convergence of the CLT via Wasserstein  distances of order 𝑟, 1 ≤ 𝑟 ≤ 3. Our bounds are in terms of Lyapunov’s coefficients and the $L^{r/2}$ fluctuation of the total conditional variances. Our Wasserstein-1 bound is optimal up to a multiplicative constant.