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Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay. (English) Zbl 1241.34089
A semilinear stochastic evolution equation driven by a Poisson random measure and a Brownian motion is considered, wherein the nonlinearity in drift and the diffusion matrix depend on the entire past trajectory. Under a condition weaker than Lipschitz, existence, uniqueness and mean square stability in initial data are established for the mild solution. An example of a stochastic nonlinear evolution equation is also given.

MSC:
34K50 Stochastic functional-differential equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
34K30 Functional-differential equations in abstract spaces
34K20 Stability theory of functional-differential equations
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