# 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 Kantorovitch-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.
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https://hal.telecom-paris.fr/hal-02098892
Contributor : Laurent Decreusefond Connect in order to contact the contributor
Submitted on : Saturday, April 13, 2019 - 2:45:22 PM
Last modification on : Tuesday, January 4, 2022 - 5:58:39 AM

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donskerLipschitz.pdf
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### Identifiers

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

### Citation

Laure Coutin, Laurent Decreusefond. Donsker's theorem in {Wasserstein}-1 distance. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2020, 25, pp.1--13. ⟨hal-02098892⟩

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