Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
By Feng-Yu Wang. 2014
57 citations recorded by the source corpus.
Abstract Consider the stochastic evolution equation in a separable Hilbert space H with 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/16181a600376cf4879ee03b8541b50a04af25e40
How researchers see this paper
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In Applied Mathematics
- Longjie Xie
- Xicheng Zhang
- Michael Röckner
- Feng-Yu Wang
- Enrico Priola
- Dario Trevisan
- Franco Flandoli
- Tusheng Zhang
In Computational Theory and Mathematics
In Finance
- Longjie Xie
- Xicheng Zhang
- Feng-Yu Wang
- Michael Röckner
- Wei Liu
- A. Budhiraja
- Paul Dupuis
- Dario Trevisan
Citations in the corpus
- Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “The interested readers are referred to [17, 18, 31, 34, 45, 52, 54] and references therein.”