| Yu Zhongming.[J].数学年刊A辑,1980,1(3-4):459~468 |
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| THE GLOBAL ASYMPTOTICAL STABILITY OF SOLUTIONOF ITO RANDOM DIFFERENTIAL EQUATION |
| Received:October 19, 1979 Revised:December 24, 1979 |
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| 英文摘要: |
| 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. |
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