Exponential stability of second-order stochastic evolution equations with Poisson jumps. (English) Zbl 1273.60077
The paper formulates conditions for mild solutions of certain second order stochastic differential equations with infinite delay and Poisson jumps to exist and to be exponentially stable in second mean.
Reviewer: Hans Crauel (Frankfurt am Main)
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 34K20 | Stability theory of functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
| 35B35 | Stability in context of PDEs |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 93E15 | Stochastic stability in control theory |
Keywords:
second order stochastic evolution equation; cosine family; mild solution; exponential stability in second mean; Poisson point processReferences:
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