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Strong completeness for a class of stochastic differential equations with irregular coefficients
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Chen, Xin and Li, X-M. (2014) Strong completeness for a class of stochastic differential equations with irregular coefficients. Electronic Journal of Probability, 19 . pp. 1-34. 90. doi:10.1214/EJP.v19-3293
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Official URL: http://dx.doi.org/10.1214/EJP.v19-3293
Abstract
We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each p > 0 there is a positive number T(p) such that for all t < T(p), the solution flow Ft(·) belongs to the Sobolev space W1,p loc . The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Stochastic differential equations | ||||||
| Journal or Publication Title: | Electronic Journal of Probability | ||||||
| Publisher: | University of Washington. Department of Mathematics | ||||||
| ISSN: | 1083-6489 | ||||||
| Official Date: | 3 October 2014 | ||||||
| Dates: |
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| Volume: | 19 | ||||||
| Number of Pages: | 34 | ||||||
| Page Range: | pp. 1-34 | ||||||
| Article Number: | 90 | ||||||
| DOI: | 10.1214/EJP.v19-3293 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Fundação para a Ciência e a Tecnologia (FCT) | ||||||
| Grant number: | EP/E058124/1 (EPSRC), PTDC/MAT/104173/2008 (FCT) |
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