Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in $\mathbb{R}^d$

Nicolas Fournier

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arXiv · 2209.00923

Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in $\mathbb{R}^d$

Nicolas Fournier

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Abstract

We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence, in expected Wasserstein distance, of the empirical measure associated to an i.i.d. $N$-sample of a given probability distribution on $\mathbb{R}^d$.

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Nicolas Fournier. 2022-09-02. Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in $\mathbb{R}^d$. https://arxiv.org/abs/2209.00923

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