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arXiv · 0806.0119

Differentiability of stochastic flow of reflected Brownian motions

Krzysztof Burdzy
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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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Krzysztof Burdzy. 2008-06-26. Differentiability of stochastic flow of reflected Brownian motions. https://arxiv.org/abs/0806.0119

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