ALMOST SURE ASYMPTOTIC STABILITY OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH JUMPS

摘要

In this paper we investigate stochastic partial differential equations with jumps in infinite dimensions. The key motivation of this paper is, under a local Lipschitz condition but without a linear growth condition, to give an existence-and-uniqueness theorem (Khasminskii-type theorem), where the classical existence-and-uniqueness result can be regarded as a special case, and then to discuss the almost sure asymptotic stability of the solutions. Moreover, as a by-product, we also derive that the solutions are weakly attracted. Finally, several examples are constructed to demonstrate our results.