Exponential behavior of solutions to stochastic integrodifferential equations with distributed delays. (English) Zbl 1316.60092
Summary: In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a \(C_{0}\)-semigroup.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H20 | Stochastic integral equations |
| 60G15 | Gaussian processes |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
stochastic integrodifferential equations; distributed delays; \(C_{0}\)-semigroup; partial functional equations; Brownian motion; mild solution; exponential decayReferences:
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