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Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients. (English) Zbl 1225.60099

Summary: 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 is also obtained. In particular, we extend N. V. Krylov and M. Röckner’s results in [Probab. Theory Relat. Fields 131, No. 2, 154–196 (2005; Zbl 1072.60050)] to the case of non-constant diffusion coefficients.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Citations:

Zbl 1072.60050
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