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.
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