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2020 Polynomial rate of convergence to the Yaglom limit for Brownian motion with drift
William Oçafrain
Electron. Commun. Probab. 25: 1-12 (2020). DOI: 10.1214/20-ECP315

Abstract

This paper deals with the rate of convergence in $1$-Wasserstein distance of the marginal law of a Brownian motion with drift conditioned not to have reached $0$ towards the Yaglom limit of the process. In particular it is shown that, for a wide class of initial measures including probability measures with compact support, the Wasserstein distance decays asymptotically as $1/t$. Likewise, this speed of convergence is recovered for the convergence of marginal laws conditioned not to be absorbed up to a horizon time towards the Bessel-$3$ process, when the horizon time tends to infinity.

Citation

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William Oçafrain. "Polynomial rate of convergence to the Yaglom limit for Brownian motion with drift." Electron. Commun. Probab. 25 1 - 12, 2020. https://doi.org/10.1214/20-ECP315

Information

Received: 7 October 2019; Accepted: 27 April 2020; Published: 2020
First available in Project Euclid: 8 May 2020

zbMATH: 1434.60012
MathSciNet: MR4095047
Digital Object Identifier: 10.1214/20-ECP315

Subjects:
Primary: 37A25, 60B10, 60J65

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