EXISTENCE, UNIQUENESS AND REGULARITY w.r.t. THE INITIAL CONDITION OF MILD SOLUTIONS OF SPDEs DRIVEN BY POISSON NOISE
Claudia Prévôt · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2010
In this paper we investigate stochastic partial differential equations in a separable Hilbert space driven by a compensated Poisson random measure. Our interest is directed towards the existence and uniqueness of mild solutions and their regularity w.r.t. the inital condition. We show the existence of a unique mild solution and prove the Gâteaux differentiability of the mild solution w.r.t. the initial condition. As a consequence, we obtain a gradient estimate for the Gâteaux derivative of the mild solution and for the resolvent associated to the mild solution.