Markov Processes

马尔可夫过程

• 批准号: 0604380
• 负责人: Srinivasa Varadhan
• 金额: --
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2009-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604380&HistoricalAwards=false
• 关键词: Markov; Processes

This proposal is partly about large deviations in different contexts. In studying the scaling limits of interacting particle limits, one usually proves laws of large numbers. They arise in different contexts and have corresponding large deviation results that are related. Random walks and diffusions in a random environment are also expected, under suitable conditions, to satisfy law of large numbers, central limit theorem and large deviations. The large deviation theory has close connection to the theory of homogenization of random Hamilton-Jacobi-Bellman equations with vanishing viscosity. We expect to continue with our investigation in these areas. In complex interactive systems, noise often acts as a stabilizing force and guides the system along a predictable deterministic path. Deviations from this behavior are rare. One goal of this project is to quantify and measure how rare a given deviation is and if such a deviation should occur what is most likely to have caused it?

这一建议部分是关于不同背景下的大偏差。在研究相互作用粒子极限的标度极限时，人们通常要证明大数定律。它们出现在不同的背景下，并有相应的大偏差的结果是相关的。 在适当的条件下，随机环境中的随机游动和扩散也期望满足大数定律、中心极限定理和大偏差。大偏差理论与粘性为零的随机Hamilton-Jacobi-Bellman方程的均匀化理论有着密切的联系。我们将继续在这些地区进行调查。在复杂的交互系统中，噪声常常起到稳定力的作用，引导系统沿着一条可预测的确定性路径运行，偏离这种行为的情况很少。本项目的一个目标是量化和测量给定偏差的罕见程度，以及如果发生这种偏差，最有可能导致它的原因是什么？