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A note on almost sure exponential stability for stochastic partial functional differential equations

Author

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  • Liu, Kai
  • Truman, Aubrey

Abstract

In a recent paper, Taniguchi (Stochastic Anal. Appl. 16 (5) (1998) 965-975) investigated the almost sure exponential stability of the mild solutions of a class of stochastic partial functional differential equations. Precisely, as small delay interval assumption is imposed, sufficient conditions are obtained there to ensure the almost sure exponential stability of the mild solutions of the given stochastic systems. Unfortunately, the main results derived by him are somewhat restrictive to be applied for practical purposes. In the note we shall prove that for a class of stochastic functional differential equations the small delay interval assumption imposed there is actually unnecessary and can be removed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:3:p:273-278
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    Cited by:

    1. Dieye, Moustapha & Diop, Mamadou Abdoul & Ezzinbi, Khalil, 2017. "On exponential stability of mild solutions for some stochastic partial integrodifferential equations," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 61-76.
    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. 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.
    4. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    5. Huabin Chen, 2015. "The existence and exponential stability for neutral stochastic partial differential equations with infinite delay and poisson jump," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 197-217, April.
    6. 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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