平稳噪声驱动下稳定流形的逼近  

Approximations of Stable Manifolds Driven by Stationary Noise

作　　者：吕文轩 陈美贤 申俊[1] LV Wenxuan;CHEN Meixian;Shen Jun(College of Mathematics,Sichuan University,Chengdu,Sichuan 610064)

机构地区：[1]四川大学数学学院,四川成都610064

出　　处：《绵阳师范学院学报》2024年第5期23-29,共7页Journal of Mianyang Teachers＇ College

基　　金：国家自然科学基金项目(12071317)。

摘　　要：文章研究一类受平稳噪声驱动的随机微分方程的动力学行为的逼近.首先证明该系统的解逐点收敛到由加性白噪声驱动的随机微分方程的解,然后证明它们的稳定流形的存在性及其逼近关系.In this paper,we study the approximation of the dynamic behavior for a class of stochastic differential equations driven by stationary noise.Firstly,we prove that the solution of stochastic differential equations converges to that of stochastic differential equations driven by additive white noise.Then,we show that the existence of stable manifolds and their approximation relationship.

关 键 词：平稳噪声 白噪声 稳定流形 随机微分方程 逼近 

分 类 号：O175.14[理学—数学]