SPDEs driven by Poisson random measure with non Lipschitz coefficients: existence results

Abstract

The article deals with SPDEs driven by Poisson random measure with non Lipschitz coefficients. Let A:E→E be a generator of an analytic semigroup on E, E being a certain Banach space. Let be a stochastic basis carrying an E-valued Poisson random measure η with characteristic measure ν and compensator γ. Let 1≤p≤2. Our point of interest is the existence of solutions to SPDE's of e.g.the following type where g:E→L(E,E 0) is some mapping satisfying ∫ E |g(x,z)−g(y,z)|p ν(dz)≤C|x−y|rp, x,y ∈ E, where 0<r<1 satisfy certain condition specified later and is again a certain Banach space.