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On stability for a class of semilinear stochastic evolution equations

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  • Liu, Kai

Abstract

Sufficient conditions for almost surely asymptotic stability with a certain decay function of sample paths, which are given by mild solutions to a class of semilinear stochastic evolution equations, are presented. The analysis is based on introducing approximating system with strong solution and using a limiting argument to pass on some properties of strong solution to our purposes. Several examples are studied to illustrate our theory. In particular, by means of the derived results we lose conditions of certain stochastic evolution systems from Haussmann (1978) to obtain the pathwise stability for mild solution with probability one.

Suggested Citation

  • Liu, Kai, 1997. "On stability for a class of semilinear stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 219-241, October.
    • Handle: RePEc:eee:spapps:v:70:y:1997:i:2:p:219-241
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    Cited by:

    1. Lv, Xiang, 2022. "Stability analysis of semilinear stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 180(C).

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