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Stochastic flows of SDEs with irregular coefficients and stochastic transport equations

✍ Scribed by Xicheng Zhang

Publisher
Elsevier Science
Year
2010
Tongue
French
Weight
324 KB
Volume
134
Category
Article
ISSN
0007-4497

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

A Stochastic Differential Equation with
A Stochastic Differential Equation with Time-Dependent and Unbounded Operator Coefficients
✍ B.V.R. Bhat; K.B. Sinha πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 511 KB

Unitary solutions of a class of stochastic equations (SDE) in Fock space with time-dependent unbounded operator coefficients are constructed as a limit of a random Trotter Kato product. Some special cases of quantum stochastic differential equations are studied as an application. 1993 Academic Press