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Boudaoui, Ahmed; Caraballo, Tomás; Ouahab, Abdelghani

Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion. (English) Zbl 1370.34137

Discrete Contin. Dyn. Syst., Ser. B 22, No. 7, 2521-2541 (2017).
Stochastic differential equations have many applications in science and engineering, and have been receiving much attention over the last decades. In this paper, the authors establish sufficient conditions ensuring existence and continuous dependence of mild solutions to first order stochastic impulsive differential equation with delays in a real separable Hilbert space. The approach is based on Banach’s fixed point theorem and Krasnoselski-Schaefer type fixed point theorem.
Reviewer: Xiaohu Wang (Chengdu)

Cited in 13 Documents

MSC:

34K50 Stochastic functional-differential equations
34K45 Functional-differential equations with impulses
34K30 Functional-differential equations in abstract spaces
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations

Keywords:

fractional Brownian motion; fixed point; mild solutions; stochastic functional differential equation
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\textit{A. Boudaoui} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 7, 2521--2541 (2017; Zbl 1370.34137)
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