Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients

Details Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients

2010-10-17

arxiv.org/abs/1010.3403v2

Mathematics

Probability

Correct a mistake in Theorem 1.3, to appear in EJP

Scientific paper

In this paper we prove the stochastic homeomorphism flow property and the strong Feller property for stochastic differential equations with sigular time dependent drifts and Sobolev diffusion coefficients. Moreover, the local well posedness under local assumptions are also obtained. In particular, we extend Krylov and R\"ockner's results in \cite{Kr-Ro} to the case of non-constant diffusion coefficients.

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