一类定常非线性随机差分方程的渐近平稳性  

Asymptotic Stationarity for a Class of Time-Invariant Non-Linear Stochastic Difference Equations

作　　者：王涛[1] 盛昭瀚[1] 

机构地区：[1]东南大学经济管理学院

出　　处：《东南大学学报（自然科学版）》1994年第2期71-77,共7页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金

摘　　要：本文应用一般状态马氏链遍历性有关理论对一类定常非线性随机差分方程的渐近平稳性问题进行分析，通过考察方程渐近平稳性质与其相应确定性部分的Ｌｙａｐｕｎｏｖ稳定性之间的联系，得到了由其相应确定性部分之Ｌｙａｐｕｎｏｖ函数判别方程本身渐近平稳（包括Ｈａｒｒｉｓ遍历、几何遍历及一致遍历等）的若干充分条件。Asymptotic stationarity of a class of time in variant non-linear stochastic differenceequations are analyzed by utilting results from the ergodic theory of general state Markov chains. Several sufficient conditions for the asymptotic stationarity which includes Harris.geometric anduniform ergodicity of the equations are derived from examing rclations between the equations’asymptotic stationarity and the Lyapunov stability of their associated deterministic parts.

关 键 词：随机差分方程 渐近平稳性 非线性 

分 类 号：O211.63[理学—概率论与数理统计]