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On exponential stability of mild solutions for some stochastic partial integrodifferential equations

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  • Dieye, Moustapha
  • Diop, Mamadou Abdoul
  • Ezzinbi, Khalil

Abstract

In this work, we study the existence and exponentially stability in p-mean square for some stochastic integrodifferential equation with delays. Also pathwise exponential stability is proved for p>2. We assume that the linear part has a resolvent operator in the sense given by Grimmer (1982). The delayed part is assumed to be continuous. Our results are proved by using the stochastic convolution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:61-76
    DOI: 10.1016/j.spl.2016.10.031
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Liu, Huoxia & Lin, Judy Yangjun, 2023. "Stochastic McKean–Vlasov equations with Lévy noise: Existence, attractiveness and stability," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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