线性I随机系统部分变元的强稳定性

Strong stability of partial variables in Itstochastic linear systems

运用随机线性系统的柯西矩阵及其截断矩阵 ,通过引进随机线性系统左截柯西矩阵和右截柯西矩阵 ,讨论了线性It^o随机系统部分变元的几乎必然强稳定性 ,得出了该系统只依赖于左截柯西矩阵的有界性和右截柯西矩阵的渐近性的各种a .s强稳定性 ,包括强稳定、强一致稳定、强渐近稳定、强一致渐近稳定及强指数稳定之间的等价条件 。

Left and right interceptive Cauchy matrices were introduced by using Cauchy matrices and its interceptive Cauchy ones. Based on the matrices, almost sure strong stability with respect to partial variables in It stochastic linear system was studied. Some equivalent criteria for different kinds of a.s. strong stability of the system were obtained. These criteria only depended on the boundedness of the left interceptive Cauchy matrices and asymptotic properties of the right ones, including strong stability, strong uniform stability, strong asymptotic stability, strong uniformly asymptotic stability and strong exponential stability.