Differentiability of stochastic flow of reflected Brownian motions

2008/06/01 by Burdzy, Krzysztof · 1 citation
#60J50 #60J65 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0806.0119

Abstract

We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map represented by a multiplicative functional for reflected Brownian motion. The method of proof is based on excursion theory and analysis of the deterministic Skorokhod equation.

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