Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

Longjie Xie; Xicheng Zhang

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arXiv · 1407.5834

Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

Longjie Xie·Xicheng Zhang

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Abstract

By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility of the associated diffusion semigroup.

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Longjie Xie, Xicheng Zhang. 2014-07-22. Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients. https://arxiv.org/abs/1407.5834

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