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Asymptotic behavior of impulsive stochastic functional differential equations

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Abstract

In this paper, a nonlinear and nonautonomous impulsive stochastic functional differential equation is considered. By establishing a nonautonomous L-operator impulsive delay inequality and using the properties of ρ-cone and stochastic analysis technique, we obtain the p-attracting set and p-invariant set of the impulsive stochastic functional differential equation. An example is also discussed to illustrate the efficiency of the obtained results.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, P. R. China

    Li Guang Xu

  2. Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310012, P. R. China

    Dan Hua He

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  1. Li Guang Xu
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  2. Dan Hua He
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Correspondence to Li Guang Xu.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11101367, 11271270, 11101298 and 11026140) and the China Scholarship Council (Grant No. 201208330001)

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Xu, L.G., He, D.H. Asymptotic behavior of impulsive stochastic functional differential equations. Acta. Math. Sin.-English Ser. 30, 1061–1072 (2014). https://doi.org/10.1007/s10114-014-1099-x

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  • DOI: https://doi.org/10.1007/s10114-014-1099-x

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