Electronic Journal of Probability

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

Xicheng Zhang

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820207

Digital Object Identifier
doi:10.1214/EJP.v16-887

Mathematical Reviews number (MathSciNet)
MR2820071

Zentralblatt MATH identifier
1225.60099

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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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References

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