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.

主要研究者将在随机过程理论的三个领域进行研究。 两个领域与大偏差理论有关。 第一个关注的问题证明了Markov随机过程具有“不连续统计”的基本大偏差原理，该类别包括不连续漂移和小扩散系数以及某些规模的排队系统的扩散。 第二个区域涉及数值和仿真方法。 研究领域与开发解决方案对Skorokhod问题的理论和应用有关，这是研究各种“受约束”随机过程的基本和有用的工具。 主要研究者将研究随机（随机）过程理论的几个领域。 其中一个领域涉及证明马尔可夫随机过程具有“不连续统计”的基本大偏差原则。 这类随机过程在随机控制的某些应用中很重要。