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Sensitivity to Small Delays of Pathwise Stability for Stochastic Retarded Evolution Equations

Author

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  • Kai Liu

    (Tianjin Normal University
    The University of Liverpool)

Abstract

In this paper, we shall study the almost sure pathwise exponential stability property for a class of stochastic functional differential equations with delays, possibly, in the highest-order derivative terms driven by multiplicative noise. Instead of establishing a moment exponential stability as the first step and then proceeding to investigate the pathwise stability of the system under consideration, we shall develop a direct approach for this problem. As a consequence, we can show that some systems, which are not exponential momently stable, have the exponential stability not sensitive to small delays in the almost sure sense.

Suggested Citation

  • Kai Liu, 2018. "Sensitivity to Small Delays of Pathwise Stability for Stochastic Retarded Evolution Equations," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1625-1646, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0750-8
    DOI: 10.1007/s10959-017-0750-8
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    Cited by:

    1. Zhi Li & Litan Yan, 2019. "Ergodicity and Stationary Solution for Stochastic Neutral Retarded Partial Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1399-1419, September.

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