Stability analysis of semilinear stochastic differential equations

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...

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Bibliographic Details
Published inStatistics & probability letters Vol. 180; p. 109257
Main Author Lv, Xiang
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2022
Subjects
Birkhoff–Khinchin ergodic theorem
Random dynamical systems
Stability theory
Stochastic differential equations
37H05
60H10
37A30
Stochastic differential equations
Random dynamical systems
Birkhoff–Khinchin ergodic theorem
34K20
Stability theory
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ISSN0167-7152
1879-2103
DOI10.1016/j.spl.2021.109257

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Summary: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2021.109257