Acta Scientiarum Naturalium Universitatis Pekinensis

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The Sublimit Distribution of Small Random Perturbed Dynamic Systems

LI Yulin, QIAN Minping   

  1. 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



  1. 北京大学数学科学学院概率统计系,北京,100871

Abstract: In this article a general framework is given in order to study the large-time behavior of a dynamic system dXt=b(Xt)dt perturbed by a small noise εdBt. The limit distribution of the perturbed system Xε 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εdBt扰动的动力系统dXt=b(Xt)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Xε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

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