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

Xiaoqin Guo

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arXiv · 2407.16980

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

Xiaoqin Guo

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Abstract

For martingales with a wide range of integrability, we will quantify the rate of convergence of the central limit theorem via Wasserstein distances of order $r$, $1\le r\le 3$. Our bounds are in terms of Lyapunov's coefficients and the $\mathscr L^{r/2}$ fluctuation of the total conditional variances. We will show that our Wasserstein-1 bound is optimal up to a multiplicative constant.

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Xiaoqin Guo. 2024-07-24. On the rate of convergence of the martingale central limit theorem in Wasserstein distances. https://arxiv.org/abs/2407.16980

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