The Sublimit Distribution of Small Random Perturbed Dynamic Systems

Acta Scientiarum Naturalium Universitatis Pekinensis

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

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

Abstract

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.

Key words: attractors, hierarchical structure, large time behavior, sublimit distribution

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

CLC Number:

O211.62

LI Yulin,QIAN Minping. The Sublimit Distribution of Small Random Perturbed Dynamic Systems[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

李玉林,钱敏平. 动力系统小扰动的次极限分布[J]. 北京大学学报（自然科学版）.

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