Stochastic flows of SDEs with irregular coefficients and stochastic transport equations
Stochastic flows of SDEs with irregular coefficients and stochastic transport equations
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DOI：
10.1016/j.bulsci.2009.12.004
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发表时间：
2009-07
影响因子：
1.3
通讯作者：
Xicheng Zhang
中科院分区：
文献类型：
--
作者：
Xicheng Zhang
In this article we study (possibly degenerate) stochastic differential equations (SDEs) with irregular (or discontinuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere stochastic (invertible) flow associated with the SDE in the sense of Lebesgue measure. In the case of constant diffusions and BV drifts, we obtain such a result by studying the related stochastic transport equation. In the case of non-constant diffusions and Sobolev drifts, we use a direct method. In particular, we extend the recent results on ODEs with non-smooth vector fields to SDEs.
