Electronic Journal of Probability

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

Xicheng Zhang

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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 Röckner's results in [10] to the case of non-constant diffusion coefficients.

Article information

Electron. J. Probab., Volume 16 (2011), paper no. 38, 1096-1116.

Accepted: 2 June 2011
First available in Project Euclid: 1 June 2016

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]

Stochastic homoemorphism flow Strong Feller property Singular drift Krylov's estimates Zvonkin's transformation

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Zhang, Xicheng. Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients. Electron. J. Probab. 16 (2011), paper no. 38, 1096--1116. doi:10.1214/EJP.v16-887. https://projecteuclid.org/euclid.ejp/1464820207

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