On the rate of convergence in Wasserstein distance of the empirical measure - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue Probability Theory and Related Fields Année : 2015

On the rate of convergence in Wasserstein distance of the empirical measure

Résumé

Let $\mu_N$ be the empirical measure associated to a $N$-sample of a given probability distribution $\mu$ on $\mathbb{R}^d$. We are interested in the rate of convergence of $\mu_N$ to $\mu$, when measured in the Wasserstein distance of order $p>0$. We provide some satisfying non-asymptotic $L^p$-bounds and concentration inequalities, for any values of $p>0$ and $d\geq 1$. We extend also the non asymptotic $L^p$-bounds to stationary $\rho$-mixing sequences, Markov chains, and to some interacting particle systems.
Fichier principal
Vignette du fichier
fournier-guillin-wass.pdf (282.15 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00915365 , version 1 (07-12-2013)

Identifiants

Citer

Nicolas Fournier, Arnaud Guillin. On the rate of convergence in Wasserstein distance of the empirical measure. Probability Theory and Related Fields, 2015, 162 (3-4), pp.707. ⟨hal-00915365⟩
616 Consultations
3173 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More