Neutral stochastic integrodifferential equations driven by a fractional Brownian motion with impulsive effects and time-varying delays. (English) Zbl 1353.60053
Summary: This paper deals with the existence, uniqueness and asymptotic behaviors of mild solutions to neutral stochastic delay functional integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion \(B^H\), with Hurst parameter \(H\in(\frac{1}{2},1)\). We use the theory of resolvent operators developed in [R. C. Grimmer, Trans. Am. Math. Soc. 273, 333–349 (1982; Zbl 0493.45015)] to show the existence of mild solutions. An example is provided to illustrate the results of this work.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H20 | Stochastic integral equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60G18 | Self-similar stochastic processes |
Keywords:
neutral stochastic integrodifferential equations; fractional Brownian motion; resolvent operators; \(C_0\)-semigroup; Wiener process; mild solutionsCitations:
Zbl 0493.45015References:
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