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Stability and Boundedness of Stochastic Volterra Integrodifferential Equations with Infinite Delay

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  • Chunmei Zhang
  • Wenxue Li
  • Ke Wang

Abstract

We make the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov‐Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and boundedness of corresponding deterministic systems under some conditions.

Suggested Citation

  • Chunmei Zhang & Wenxue Li & Ke Wang, 2013. "Stability and Boundedness of Stochastic Volterra Integrodifferential Equations with Infinite Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:320832
    DOI: 10.1155/2013/320832
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    References listed on IDEAS

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    1. Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
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