Mathematical Sciences: Research on Stochastic Process and Large Deviation Theory

数学科学：随机过程与大偏差理论研究

• 批准号: 8902333
• 负责人: Paul Dupuis
• 金额: $ 3.45万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902333&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Stochastic; Process

The principal investigator will conduct research in three areas of the theory of stochastic processes. Two areas have to do with large deviation theory. The first concerns proving the fundamental large deviation principle for Markov stochastic processes with "discontinuous statistics", a class that includes diffusions with discontinuous drift and small diffusion coefficient as well as certain scaled queueing systems. The second area involves numerical and simulation methods. The third area of study is concerned with developing the theory and applications of the solution to the Skorokhod Problem, which is a basic and useful tool in the study of various "constrained" stochastic processes. The principal investigator will study several areas of the theory of stochastic (random) processes. One of the areas involves proving the fundamental large deviation principle for Markov stochastic processes with "discontinuous statistics". This class of stochastic processes is important in certain applications of stochastic control.

首席研究员将在三个方面进行研究 随机过程理论的领域。 两个领域必须 与大偏差理论有关。 第一个问题是证明 马尔可夫随机过程的基本大偏差原理 使用“不连续统计”处理，这是一个类，包括 不连续漂移小扩散 系数以及某些缩放的缩放系统。 的 第二个领域涉及数值和模拟方法。 的 第三个研究领域是关于发展理论， 解决Skorokhod问题的方法， 一个基本的和有用的工具，在研究各种“约束” 随机过程 首席研究员将研究的几个领域， 随机过程（Random Processes） 的地区之一 包括证明基本的大偏差原理， 马尔可夫随机过程与“不连续统计”。 这类随机过程在某些情况下很重要。 随机控制的应用