---
abstract: 'We use Stein’s method to bound the Wasserstein distance of order $2$ between a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic process $(X_t)_{t \geq 0}$ satisfies an additional exchangeability assumption, we show it can also be used to obtain bounds on Wasserstein distances of any order $p \geq 1$. Using our results, we provide optimal convergence rates for the multi-dimensional Central Limit Theorem in terms of Wasserstein distances of any order $p \geq 2$ under simple moment assumptions.'
author:
- |
    Thomas Bonis\
    DataShape team, Inria Saclay, Université Paris-Saclay, Paris, France\
    thomas.bonis@inria.fr
bibliography:
- 'Bibliography.bib'
title:
- 'Stein’s method for normal approximation in Wasserstein distances with application to the multivariate Central Limit Theorem [^1] '
- 'Stein’s method for normal approximation in Wasserstein distances with application to the multivariate Central Limit Theorem'
---

Acknowledgements {#acknowledgements .unnumbered}
================

The author would like to thank Michel Ledoux for his many comments and advice regarding the redaction of this paper as well as Jérôme Dedecker and Yvik Swan, Chi Tran and Frédéric Chazal for their multiple remarks.

[^1]: The author was supported by the French Délégation Générale de l’Armement (DGA) and by ANR project TopData ANR-13-BS01-0008.
