Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients
Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients
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DOI：
10.1214/ejp.v16-887
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发表时间：
2010-10
影响因子：
1.4
通讯作者：
Xicheng Zhang
中科院分区：
文献类型：
--
作者：
Xicheng Zhang
本文证明了具有Sobolev扩散系数和奇异时变漂移的随机微分方程的随机同胚流性质和强Feller性质。此外，在局部假设下也得到了局部适定性。特别地，我们将Krylov和Rockner在[10]中的结果推广到扩散系数为非常数的情况。
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 Rockner's results in [10] to the case of non-constant diffusion coefficients.