The Asymptotic Stability Of One-dimensional Linear Stochastic Differential Equations

In this paper,we study the asymptotic stability for one-dimensional linear stochastic differential equations,and derive the mean-square asymptotic stability and divergence conditions of solutions for the equations with constant coefficient and variable coefficient.Firstly,we introduce the stability theory of ordinary differential equations and the definition,method,application of exponential dichotomy.At the same time,we introduce the definition and relevant results of exponential dichotomy of It(?) stochastic differential equations.In one-dimensional case,exponential dichotomy is equivalent to exponential asymptotic stability or exponential asymptotic divergence.Finally,we obtain the mean-square asymptotic stability and divergence conditions of the solutions for It(?) stochastic differential equations.