Donsker's theorem in {Wasserstein}-1 distance
Probability
2025-04-29 v1
Abstract
We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulus of the solution of the Stein's equation. As an application, we can evaluate the rate of convergence towards the local time at 0 of the Brownian motion.
Keywords
Cite
@article{arxiv.1904.07045,
title = {Donsker's theorem in {Wasserstein}-1 distance},
author = {L. Coutin and Laurent Decreusefond},
journal= {arXiv preprint arXiv:1904.07045},
year = {2025}
}