White Noise Approach to Evolution Equations Driven by Hilbert Space Valued Levy White Noise

We develop a white noise framework and the theory of stochastic test function and distribution spaces for Hilbert space valued Levy processes in order to study stochastic evolution equations in these spaces driven by Levy white noise. This allows for a generalization of the classical solution concepts to solutions in the sense of stochastic distributions. For exapmle, the Heat equation driven by Levy white noise always has a solution in stochastic distribution spaces while it is easy to see that a classical solution only exists in special cases.