Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay (Q635804)
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scientific article; zbMATH DE number 5942038
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay |
scientific article; zbMATH DE number 5942038 |
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Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay (English)
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23 August 2011
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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.
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stochastic evolution equations
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infinite delay
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mild solutions
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existence
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uniqueness
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stability with respect to initial condition
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