Regularity of stochastic kinetic equations
Electronic Journal of Probability, ISSN: 1083-6489, Vol: 22, Issue: 0
2017
- 24Citations
- 4Captures
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Article Description
We consider regularity properties of stochastic kinetic equations with multiplicative noise and drift term which belongs to a space of mixed regularity (L -regularity in the velocity-variable and Sobolev regularity in the space-variable). We prove that, in contrast with the deterministic case, the SPDE admits a unique weakly differentiable solution which preserves a certain degree of Sobolev regularity of the initial condition without developing discontinuities. To prove the result we also study the related degenerate Kolmogorov equation in Bessel-Sobolev spaces and construct a suitable stochastic flow.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85021648592&origin=inward; http://dx.doi.org/10.1214/17-ejp65; https://projecteuclid.org/euclid.ejp/1496196076; https://projecteuclid.org/download/pdfview_1/euclid.ejp/1496196076; https://projecteuclid.org/journals/electronic-journal-of-probability/volume-22/issue-none/Regularity-of-stochastic-kinetic-equations/10.1214/17-EJP65.full; https://dx.doi.org/10.1214/17-ejp65; https://projecteuclid.org/access-suspended
Institute of Mathematical Statistics
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