Well-posedness for a class of dissipative stochastic evolution equations with Wiener and Poisson noise

Details Well-posedness for a class of dissipative stochastic evolution equations with Wiener and Poisson noise Well-posedness for a class of dissipative stochastic evolution equations with Wiener and Poisson noise

2011-10-18

arxiv.org/abs/1110.4100v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

We prove existence and uniqueness of mild and generalized solutions for a class of stochastic semilinear evolution equations driven by additive Wiener and Poisson noise. The non-linear drift term is supposed to be the evaluation operator associated to a continuous monotone function satisfying a polynomial growth condition. The results are extensions to the jump-diffusion case of the corresponding ones proved in [4] for equations driven by purely discontinuous noise.

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