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Exponential stability of impulsive stochastic partial differential equations with delays

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  • Li, Dingshi
  • Fan, Xiaoming

Abstract

In this paper, we are concerned with the exponential stability problem of impulsive control stochastic partial differential equations with delays. By employing the formula for the variation of parameters and inequality technique, several criteria on exponential stability are derived and the exponential convergence rate is estimated. Some examples are given to illustrate the theoretical results and to show that the criteria can be applied to stabilize the continuous system with delays, which may be unstable.

Suggested Citation

  • Li, Dingshi & Fan, Xiaoming, 2017. "Exponential stability of impulsive stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 185-192.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:185-192
    DOI: 10.1016/j.spl.2017.03.016
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    References listed on IDEAS

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    1. 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.
    2. Liu, Kai & Truman, Aubrey, 2000. "A note on almost sure exponential stability for stochastic partial functional differential equations," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 273-278, November.
    3. Long, Shujun & Teng, Lingying & Xu, Daoyi, 2012. "Global attracting set and stability of stochastic neutral partial functional differential equations with impulses," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1699-1709.
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    Cited by:

    1. Marino, L. & Menozzi, S., 2023. "Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 106-170.

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