Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise
By Carlo Marinelli, Claudia Prévôt, Michael Röckner. 2008
106 citations recorded by the source corpus.
Abstract We prove existence, uniqueness and Lipschitz dependence on the initial datum for mild solutions of stochastic partial differential equations with Lipschitz coefficients driven by Wiener and Poisson noise. Under additional assumptions, we prove Gâteaux and Frechet differentiability of solutions with respect to the initial datum. As an application, we obtain gradient estimates for the resolvent associated to the mild solution. Finally, we prove the strong Feller property of the associated semigroup.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/f0b72c00511b836a58624f24914b526736dd0da1
How researchers see this paper
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In Computational Theory and Mathematics
- Carlo Marinelli
- Michael Röckner
- Wei Liu
- Feng-Yu Wang
- Giuseppe Da Prato
- Xicheng Zhang
- Vladimir Bogachev
- Franco Flandoli
In Control and Systems Engineering
- Michael Röckner
- Carlo Marinelli
- Xicheng Zhang
- Franco Flandoli
- Giuseppe Da Prato
- Wei Liu
- Sandra Cerrai
- Longjie Xie
In Finance
- Carlo Marinelli
- Michael Röckner
- Wei Liu
- Tusheng Zhang
- Feng-Yu Wang
- Benjamin Gess
- Giuseppe Da Prato
- Wei David Liu
Citations in the corpus
- On Maximal Inequalities for Purely Discontinuous Martingales in Infinite Dimensions (2013, methodology): “In fact, while we refer to Section 6 below for details, it seems important to remark already at this stage that the estimates which we termed “Bichteler-Jacod’s inequalities” in our previous article [23] should have probably more Department of Mathematics, University College London, Gower Street, Lo”