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

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

2008-08-11

arxiv.org/abs/0808.1509v1

Mathematics

Probability

26 pages

Scientific paper

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.

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