Differentiability of stochastic flow of reflected Brownian motions

Krzysztof Burdzy

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Differentiability of stochastic flow of reflected Brownian motions

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arxiv 0806.0119 v2 pith:3FGTTD3R submitted 2008-06-01 math.PR

Differentiability of stochastic flow of reflected Brownian motions

Krzysztof Burdzy This is my paper

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keywords brownianreflectedflowmotionsstochasticanalysisderivativedeterministic

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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.

Differentiability of stochastic flow of reflected Brownian motions

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