动力系统小扰动的次极限分布

北京大学学报（自然科学版）

动力系统小扰动的次极限分布

李玉林,钱敏平

北京大学数学科学学院概率统计系，北京，100871

收稿日期:1997-08-25 出版日期:1999-01-20 发布日期:1999-01-20

The Sublimit Distribution of Small Random Perturbed Dynamic Systems

LI Yulin, QIAN Minping

Dept. of Prob. and Stat., School of Mathematical Sciences, Peking University, Beijing, 100871, China

Received:1997-08-25 Online:1999-01-20 Published:1999-01-20

摘要/Abstract

摘要： 给出了一个一般框架以研究经小噪声εdB_t扰动的动力系统dX_t=b(X_t)dt的长期行为。通过吸引子的分层结构粗略地描述了扰动的系统X^ε在时刻t ～exp(c/ε²)时的分布在ε→0时的极限。

关键词: 吸引子, 分层结构, 长期行为, 次极限分布

Abstract: In this article a general framework is given in order to study the large-time behavior of a dynamic system dX_t=b(X_t)dt perturbed by a small noise εdBt. The limit distribution of the perturbed system X^ε at time t ～exp(c/ε²) as ε→0 is roughly described through the hierarchy structure of attractors.