Multiplicative functional for reflected Brownian motion via deterministic ODE

2010/01/01 by Krzysztof Burdzy, John M. Lee · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Stochastic processes and financial applications

paper · pdf · doi:10.1215/ijm/1336049981

crossref issued 2010/01/01 · crossref published 2010/01/01 · crossref published-print 2010/01/01 · openalex publication_date 2010/01/01 · crossref created 2019/03/01 · crossref deposited 2024/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/21 · crossref indexed 2026/07/28

Abstract

We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the corresponding stochastic flow. The method of proof is based on a study of the deterministic version of the problem and the excursion theory.

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