Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise

Marinelli, Carlo; Prévôt, Claudia; Röckner, Michael

Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise

Authors

Marinelli, Carlo

Prévôt, Claudia

Röckner, Michael

Description

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 Gateaux 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.
26 pages