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

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Article number	27
Journal	Electronic Communications in Probability
Volume	25
DOIs	https://doi.org/10.1214/20-ECP308
Publication status	Published - 1 Jan 2020

Keywords

Donsker theorem
Malliavin calculus
Stein’s method
Wasserstein distance

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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",

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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

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

Abstract

Keywords

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