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2020 Donsker’s theorem in Wasserstein-1 distance
Laure Coutin, Laurent Decreusefond
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP308

Abstract

We compute the Wassertein-1 (or Kantorovitch-Rubinstein) distance between a random walk in $\mathbf{R} ^{d}$ and the Brownian motion. The proof is based on a new estimate of the modulus of continuity 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 and to a Brownian bridge.

Citation

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Laure Coutin. Laurent Decreusefond. "Donsker’s theorem in Wasserstein-1 distance." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP308

Information

Received: 16 August 2019; Accepted: 11 March 2020; Published: 2020
First available in Project Euclid: 31 March 2020

zbMATH: 1434.60100
MathSciNet: MR4089734
Digital Object Identifier: 10.1214/20-ECP308

Subjects:
Primary: 60F15
Secondary: 60G15, 60G55, 60H07

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