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

Nicolas Fournier (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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 $\mathbb{R}^d$.

Domaines: Probabilités [math.PR]

Nicolas Fournier. Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in $\mathbb{R}^d$. ESAIM: Probability and Statistics, 2023, 27, pp.749-775. ⟨10.1051/ps/2023011⟩. ⟨hal-03768963⟩