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Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process. (English) Zbl 1435.34074

Summary: The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed in this work by using the Banach fixed point theorem and the theory of resolvent operator developed by R. C. Grimmer [Trans. Am. Math. Soc. 273, 333–349 (1982; Zbl 0493.45015)]. Furthermore, the exponential stability in mean square for the mild solution to neutral stochastic integro-differential equations with Rosenblatt process is obtained by establishing an integral inequality. Finally, an example is exhibited to illustrate the abstract theory.

MSC:

34K30 Functional-differential equations in abstract spaces
34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
34K45 Functional-differential equations with impulses
34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
45K05 Integro-partial differential equations
47N20 Applications of operator theory to differential and integral equations

Citations:

Zbl 0493.45015
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References:

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