Stochastic flows of SDEs with irregular coefficients and stochastic transport equations
By Xicheng Zhang. 2009
79 citations recorded by the source corpus.
Abstract 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.
Subfields: Applied Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/cb92178e3a7dacc1f1bb1fadaa311c93af731042
How researchers see this paper
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In Applied Mathematics
- Dario Trevisan
- Xicheng Zhang
- Michael Röckner
- Longjie Xie
- Enrico Priola
- Franco Flandoli
- Feng-Yu Wang
- Tusheng Zhang
In Finance
- Dario Trevisan
- Xicheng Zhang
- Michael Röckner
- Feng-Yu Wang
- Longjie Xie
- Wei Liu
- A. Budhiraja
- Paul Dupuis
Citations in the corpus
- Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients (2010, background): “In the papers [9], [28], and [23], the vector field b needs to be in W 1,q loc (R ) for some q > 1.”
- Well-posedness of Multidimensional Diffusion Processes with Weakly Differentiable Coefficients (2015, methodology): “Crippa-DeLellis’ technique [14] was extended to SDE’s in [35, 28]): of course, novelties and improvements appear in these developments, but to the author’s knowledge that they address different aspects (such as strong solutions, equations with jumps, quantitative estimates, etc.”