Donsker’s theorem in wasserstein-1 distance

Laure Coutin; Laurent Decreusefond

doi:10.1214/20-ECP308

Donsker’s theorem in wasserstein-1 distance

Laure Coutin
, Laurent Decreusefond

Université de Toulouse

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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 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.

langue originale	Anglais
Numéro d'article	27
journal	Electronic Communications in Probability
Volume	25
Les DOIs	https://doi.org/10.1214/20-ECP308
état	Publié - 1 janv. 2020

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10.1214/20-ECP308

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@article{17b958b7a93b4cea97dc55bb66b337e0,

title = "Donsker{\textquoteright}s theorem in wasserstein-1 distance",

abstract = "We compute the Wassertein-1 (or Kantorovitch-Rubinstein) distance between a random walk in Rd and the Brownian motion. The proof is based on a new estimate of the modulus of continuity of the solution of the Stein{\textquoteright}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.",

keywords = "Donsker theorem, Malliavin calculus, Stein{\textquoteright}s method, Wasserstein distance",

author = "Laure Coutin and Laurent Decreusefond",

year = "2020",

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doi = "10.1214/20-ECP308",

language = "English",

volume = "25",

journal = "Electronic Communications in Probability",

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AU - Coutin, Laure

AU - Decreusefond, Laurent

PY - 2020/1/1

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N2 - We compute the Wassertein-1 (or Kantorovitch-Rubinstein) distance between a random walk in Rd 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.

AB - We compute the Wassertein-1 (or Kantorovitch-Rubinstein) distance between a random walk in Rd 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.

KW - Donsker theorem

KW - Malliavin calculus

KW - Stein’s method

KW - Wasserstein distance

UR - https://www.scopus.com/pages/publications/85084126876

U2 - 10.1214/20-ECP308

DO - 10.1214/20-ECP308

M3 - Article

AN - SCOPUS:85084126876

SN - 1083-589X

VL - 25

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

M1 - 27

ER -

Donsker’s theorem in wasserstein-1 distance

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