Martingale central limit theorems in $p$-Wasserstein distance
Holder： Xiao Fang（the Chinese University of Hong Kong）
Time：2026-11-12 14:00-15:00
Location：智华楼四元厅-225
Abstract:
We obtain multivariate martingale central limit theorems in $p$-Wasserstein distance with respect to the $\ell_r$ norm in $\mathbb{R}^d$ for $p\geq 1$ and $r\in [1,\infty]$, which generalize the results for $p=1$ and $r=2$ in the literature.
As corollaries, we obtain the Yurinskii coupling and Cram\'er-type moderate deviation results. We also provide an illustrative application to the stochastic gradient descent algorithm. To prove our main results, we combine Lindeberg's swapping argument with a new Gaussian convolution inequality controlling the $p$-Wasserstein distance between a Gaussian convolved with a perturbation and the Gaussian with matching mean and covariance matrix. The latter is obtained by developing the recent line of research on $p$-Wasserstein bounds and exhibits optimal dependence on $p$ and optimal moment requirements for the perturbation.
About the Speaker:
Xiao Fang is an associate professor in the Department of Statistics and Data Science at the Chinese University of Hong Kong. His research interests include asymptotic theory in probability and statistics, Stein’s method for distributional approximations, and multivariate and high-dimensional central limit theorems.
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