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Stability analysis of semilinear stochastic differential equations

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  • Lv, Xiang

Abstract

This paper is concerned with the global stability of semilinear stochastic differential equations (SDEs) with multiplicative white noise, which is a continuation of our recent work published in SIAM Journal on Control and Optimization, 2018. Under an explicit condition that the Lipschitz constant of nonlinear term is smaller than the top Lyapunov exponent of the linear random dynamical system (RDS), we prove that the zero solution is globally stable.

Suggested Citation

  • Lv, Xiang, 2022. "Stability analysis of semilinear stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s0167715221002194
    DOI: 10.1016/j.spl.2021.109257
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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