In this paper we are interested in a reaction diffusion equation driven by Poissonian noise respective L\'evy noise. For this aim we first show existence of a martingale solution for an SPDE of parabolic type driven by a Poisson random measure with only continuous and bounded coefficients. This result is transferred to an parabolic SPDE driven by L\'evy noise. In a second step, we show existence of a martingale solution of reaction diffusion type, also driven by Poissonian noise respective L\'evy noise. Our results answer positively a long standing open question about existence of martingale solutions driven by genuine L\'evy processes.
|Number of pages||79|
|Publication status||Published - Oct 2010|