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Existence and exponential stability of a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps

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  • Chen, Guiling
  • van Gaans, Onno
  • Lunel, Sjoerd Verduyn

Abstract

In this paper, the existence, uniqueness and exponential stability of mild solution for a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps are studied. The existence and uniqueness of mild solution are studied by means of successive approximations, and the exponential stability in pth moment of mild solution is investigated by employing an appropriate impulsive-integral inequality. An example is given to illustrate our main results.

Suggested Citation

  • Chen, Guiling & van Gaans, Onno & Lunel, Sjoerd Verduyn, 2018. "Existence and exponential stability of a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 7-18.
    • Handle: RePEc:eee:stapro:v:141:y:2018:i:c:p:7-18
    DOI: 10.1016/j.spl.2018.05.017
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    References listed on IDEAS

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    1. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    2. Chen, Huabin, 2010. "Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 50-56, January.
    3. Cui, Jing & Yan, Litan & Sun, Xichao, 2011. "Exponential stability for neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1970-1977.
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    Cited by:

    1. Ting Cai & Pei Cheng, 2021. "Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses," Mathematics, MDPI, vol. 9(4), pages 1-15, February.

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