Stochastic lof SDEs with singular drifts and sobolev diffusion coefficients

Xicheng Zhang

doi:10.1214/EJP.v16-887

Stochastic lof SDEs with singular drifts and sobolev diffusion coefficients

Xicheng Zhang^*

^*Corresponding author for this work

Wuhan University

Research output: Contribution to journal › Article › peer-review

87 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1096-1116
Number of pages	21
Journal	Electronic Journal of Probability
Volume	16
DOIs	https://doi.org/10.1214/EJP.v16-887
Publication status	Published - 1 Jan 2011
Externally published	Yes

Keywords

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

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10.1214/EJP.v16-887

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AB - 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.

KW - Krylov’s estimates

KW - Singular drift

KW - Stochastic homoemorphism flow

KW - Strong Feller property

KW - Zvonkin’s transformation

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Stochastic lof SDEs with singular drifts and sobolev diffusion coefficients

Abstract

Keywords

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