# Donsker's theorem in {Wasserstein}-1 distance

4 DIG - Data, Intelligence and Graphs
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in $R^d$ 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 :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [17 references]

https://hal.telecom-paristech.fr/hal-02098892
Contributor : Laurent Decreusefond <>
Submitted on : Saturday, April 13, 2019 - 2:45:22 PM
Last modification on : Thursday, October 17, 2019 - 12:36:59 PM

### Files

donskerLipschitz.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-02098892, version 1
• ARXIV : 1904.07045

### Citation

L. Coutin, Laurent Decreusefond. Donsker's theorem in {Wasserstein}-1 distance. 2019. ⟨hal-02098892⟩

Record views