随机中立型泛函微分方程的渐近性质

Asymptotic Properties of Neutral Stochastic Functional Differential Equations

本文研究了—般随机中立型泛函微分方程解的渐近性质,利用Lyapunov函数和半鞅收敛定理,建立了该方程解的一些渐近稳定性、多项式渐近稳定性及指数稳定性的充分性判据, 其条件无需算子LV负定,并且利用了随机扰动项在稳定性中所起的有益作用,其结果涵盖并推广了已有文献的结论．

The asymptotic properties of one type of neutral stochastic functional differential equations have been discussed in this paper. By Lyapunov function and semimartingale convergence theorem, some results on its properties such as asymptotic stabilities, polynomial stabilities and exponential stabilities have been given. The conditions need no negative -definite operator of LV, and the beneficial work of stochastic paterbation item on stability has been used well. All the results imply and generalize those conclusions existed in references.