Mathematical Sciences: Research in Stochastic Process Theory

数学科学：随机过程理论研究

• 批准号: 9115762
• 负责人: Paul Dupuis
• 金额: $ 7.2万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9115762&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 and related partial differential equations. The first area is concerned with proving the 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 considers the problem of obtaining the full asymptotic expansion for certain important classes of jump Markov processes. The last part of the proposed work involves research in the area of numerical methods for continuous time stochastic control problems. The principal investigator will conduct research on several problems that are at the interface of stochastic processes, a branch of probability theory, and stochastic control, a branch of applied mathematics. The problems are motivated by issues involved with understanding systems of queues, which arise naturally in several applications, for example communications.

首席研究员将在随机过程理论和相关偏微分方程的三个领域进行研究。第一个领域是用“不连续统计量”证明马尔可夫随机过程的大偏差原理，这类过程包括具有不连续漂移和小扩散系数的扩散以及某些尺度排队系统。第二个领域考虑了某些重要的跳跃马尔可夫过程的完全渐近展开式问题。最后一部分工作涉及连续时间随机控制问题的数值方法领域的研究。首席研究员将对随机过程(概率论的一个分支)和随机控制(应用数学的一个分支)之间的几个问题进行研究。这些问题的动机是与理解队列系统有关的问题，这些问题在几个应用程序中自然出现，例如通信。