Stochastic Averaging: Geometry and Stratified Spaces

随机平均：几何和分层空间

• 批准号: 0071484
• 负责人: Richard Sowers
• 金额: $ 8.8万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071484&HistoricalAwards=false
• 关键词: Stochastic; Averaging; Geometry; Stratified; Spaces

This research centers around some problems in the technique of model reduction known as stochastic averaging. Although stochastic averaging has been around for at least 30 years, recent developments in stochastic analysis suggest a new look at it. In particular, it is now clear that the reduced model can take values in a stratified space. This proposal outlines a number of questions, with the goal of a better understanding of both stochastic averaging and Markov processes on stratified spaces. Roughly, the proposed research attempts to better understand the effects of small noise upon oscillations. As many mechanical, manufacturing, and biological systems have oscillatory behavior affected by small noise, the proposed research can inform our understanding and design of a host of systems. The more particular goal of this research is to find accurate methods of simplifying more complicated models. These simplified models could then be used in control and design procedures.

本研究主要围绕模型简化技术中的一些问题，即随机平均。尽管随机平均已经存在了至少30年，但随机分析的最新发展让人们对它有了新的认识。特别是，现在很清楚，简化模型可以在分层空间中取值。本建议概述了一些问题，目的是更好地理解分层空间上的随机平均和马尔可夫过程。粗略地说，提出的研究试图更好地理解小噪声对振荡的影响。由于许多机械、制造和生物系统都有受小噪声影响的振荡行为，因此所提出的研究可以为我们对许多系统的理解和设计提供信息。本研究的更具体目标是找到简化更复杂模型的准确方法。这些简化的模型可以用于控制和设计过程。