Rate of convergence of the conditioned random walk towards the Brownian bridge

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Laurent Decreusefond, Antonin Jacquet
DOI: 10.48550/arxiv.2601.11162
Cited by: 0

Abstract

We study the rate of convergence of two discrete processes towards the Brownian bridge: the random walk conditioned to be zero at time 2n and the empirical process which appears in the Glivencko-Cantelli theorem. Combining a functional Stein method with a Radon-Nikodym representation of the bridge, we bound the Fortet-Mourier distance between these conditioned processes and the Brownian bridge.

Fields of Study & Subjects

Stochastic processes and statistical mechanics Probability and Statistical Research Stochastic processes and financial applications

Publication details

Journal / source
arXiv (Cornell University)
Publication date
16 January 2026
Language
EN
Document type
Preprint