THE GLOBAL ASYMPTOTICAL STABILITY OF SOLUTIONOF ITO RANDOM DIFFERENTIAL EQUATION
Citation：
Yu Zhongming.THE GLOBAL ASYMPTOTICAL STABILITY OF SOLUTIONOF ITO RANDOM DIFFERENTIAL EQUATION[J].Chinese Annals of Mathematics B,1980,1(3-4):459~468
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Authors：
Yu Zhongming;
Abstract：
In this paper we discuss the stability and global asymptotical stability of the solu-
tion of It? random differeirtial equation \[\left\{ \begin{array}{l}
d\xi (t) = b(\xi (t),t)dt + \sigma (\xi (t),t)dw(t)\\xi ({t_0}) = {\xi _0}
\end{array} \right.\]
here \({\xi _0}\) is a bounded random vector. Suffloient conditions for the existence of the two typical stability are given. These conditions are natural extension of Lyapunov function in deterministic system. Our results extend some results due to Friedman, and pinsky (see[l]). We suggest an opinion about definition of asymptotical stability of solution of the following It? random differential equation
\[\left\{ \begin{array}{l}
d\xi (t) = b(\xi (t)dt + \sigma (\xi (t))dw(t)\\xi ({t_0}) = {x_0}
\end{array} \right.\]
where \({x_0}\) is a point of n-dimensional Eiiolidian space.
