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Exponential stability of non-linear stochastic evolution equations

Author

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  • Liu, Kai
  • Mao, Xuerong

Abstract

The aim of this paper is to investigate exponential stability of paths for a class of Hilbert space-valued non-linear stochastic evolution equations. The analyses consist in using exponential martingale formula, Lyapunov functional and some special inequalities derived for our stability purposes. Various sufficient conditions are obtained to ensure the stability of the strong solutions. Several applications to stochastic partial differential equations are studied to illustrate our theory. In particular, by means of our results we loosen the conditions of certain stochastic evolution systems from Haussmann (1978) or Ichikawa (1982).

Suggested Citation

  • Liu, Kai & Mao, Xuerong, 1998. "Exponential stability of non-linear stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 173-193, November.
    • Handle: RePEc:eee:spapps:v:78:y:1998:i:2:p:173-193
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    Citations

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    Cited by:

    1. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    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. Appleby, John A. D. & Reynolds, David W., 2003. "Non-exponential stability of scalar stochastic Volterra equations," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 335-343, May.
    4. Lv, Xiang, 2022. "Stability analysis of semilinear stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 180(C).
    5. Bergé, Benjamin & D. Chueshov, Igor & Vuillermot, Pierre-A., 2001. "On the behavior of solutions to certain parabolic SPDE's driven by wiener processes," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 237-263, April.
    6. Wan, Li & Duan, Jinqiao, 2008. "Exponential stability of non-autonomous stochastic partial differential equations with finite memory," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 490-498, April.

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