| Issue |
ESAIM: PS
Volume 27, 2023
|
|
|---|---|---|
| Page(s) | 749 - 775 | |
| DOI | https://doi.org/10.1051/ps/2023011 | |
| Published online | 08 August 2023 | |
Convergence of the empirical measure in expected wasserstein distance: non-asymptotic explicit bounds in ℝd
Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistiques et Modélisation, 75005 Paris, France
* Corresponding author: nicolas.fournier@sorbonne-universite.fr
Received:
2
September
2022
Accepted:
28
April
2023
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 ℝd.
Mathematics Subject Classification: 60F25 / 65C05
Key words: Empirical measure / sequence of i.i.d. random variables / optimal transportation
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.