On bounded mild solution for a class of semilinear stochastic partial differential equation driven by Levy and stable processes
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We show the existence and uniqueness of bounded mild solutions for a class of semilinear stochastic partial differential equations driven by a general class of Levy processes including the square and the square integrable cases (like the alpha stable processes) under local Lipschitz, linear growth, Holder conditions on the coefficients. This is done using stochastic analysis tools for jumps processes with particular attention to the non square integrable case through a truncation method by separating the small and big jumps on a given arbitrary level together with a use of classical fixed point theorem. Finally, we give an example to show the usefulness of the theoritical results that we obtain in this paper.
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