不动点与随机时滞微分方程的稳定性  

Fixed points and stability of stochastic delay differential equations

作　　者：罗交晚[1] 蓝国烈[1] 

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2008年第3期6-9,共4页Journal of Guangzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10671043)

摘　　要：考虑一类线性变时滞随机微分方程,利用不动点理论,给出了零解均方渐近稳定的条件.这些条件不要求时滞有界,也不要求方程的系数函数不变号.证明了一个带有充分必要条件的均方渐近稳定性定理,改进和推广了一些相关文献的结果.In this paper we consider a linear scalar stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved. Some well-known results are improved and generalized.

关 键 词：不动点 稳定性 随机微分方程 变时滞 

分 类 号：O211.63[理学—概率论与数理统计]