Journal article 1697 views
Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
Journal of Differential Equations, Volume: 260, Issue: 3, Pages: 2792 - 2829
Swansea University Author: Feng-yu Wang
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DOI (Published version): 10.1016/j.jde.2015.10.020
Abstract
Consider the stochastic evolution equation in a separable Hilbert space Hwith a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution. Under a reasonable condition ensuring the non-explosion of t...
| Published in: | Journal of Differential Equations |
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| ISSN: | 0022-0396 |
| Published: |
Elsevier BV
2016
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa28388 |
| Abstract: |
Consider the stochastic evolution equation in a separable Hilbert space Hwith a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution. Under a reasonable condition ensuring the non-explosion of the solution, the strong Feller property of the associated Markov semigroup is proved. Gradient estimates and log-Harnack inequalities are derived for the associated semigroup under certain global conditions, which are new even in finite-dimensions. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
3 |
| Start Page: |
2792 |
| End Page: |
2829 |