Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure

Details Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure

2010-10-28

arxiv.org/abs/1010.5933v1

Mathematics

Probability

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Scientific paper

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.

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