Support theorem for the solution of a white-noise-driven parabolic stochastic partial differential equation with temporal Poissonian jumps

Abstract

We study the weak solution X of a parabolic stochastic partial differential equation driven by two independent processes: a Gaussian white noise and a finite Poisson measure. We characterize the support of the law of X as the closure in \mathbb{D}≤ft( [0,T], \mathbb{C}([0,1])\right), endowed with its Skorokhod topology, of a set of weak solutions of ordinary partial differential equations.