Mathematical Sciences: Research on Stochastic Processes and Optimization

数学科学：随机过程和优化研究

• 批准号: 9403820
• 负责人: Paul Dupuis
• 金额: $ 8.3万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-01 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9403820&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Stochastic; Processes

This research is divided into two parts. The first part considers problems from the theory of large deviations. This theory seeks to estimate and characterize rare events in stochastic systems. The focus of the work is on extending some recently developed methods. In this new approach the large deviation problem is recast in terms of the limiting behavior of a sequence of stochastic variational problems. A problem of particular interest is the analysis of large deviation properties of queuing systems. The second part of the proposal discusses the development of stochastic process models for what are called "interacting users of a resource system." These models describe situations in which there are a large number of users of a finite set of resources. Examples occur in economics, finance and transportation. The goals of the work are development of the models, limit theorems, and model simplification. This research is divided into two parts. The first part considers problems from the theory of large deviations. This theory seeks to estimate and characterize rare events in stochastic systems. Such rare events can play a critical role in determining the performance of many systems modeled by stochastic processes. A problem of compelling interest is the analysis of large deviation properties of queuing systems, and in particular those that arise in communication systems. At the same time, large deviation theory is thought to have great potential in the analysis and design of high speed networks (including ATM networks). The focus of the work is on extending some recently developed methods that can handle this difficult class of problems. The second part of the research involves the development of stochastic process models for what we call "interacting users of a resource system." These models describe situations in which there are a large number of users of a finite set of resources. Examples occur in economics, finance and transportation. Such dynamical models are needed t o predict how the population of users would adapt to changes in the environment. The main goal of this part of the proposal is the development of the models and model simplification.

本研究分为两个部分。第一部分从大偏差理论的角度思考问题。这一理论试图估计和刻画随机系统中的罕见事件。工作的重点是对最近开发的一些方法进行扩展。在这种新方法中，大偏差问题被重塑为一系列随机变分问题的极限行为。一个特别感兴趣的问题是对排队系统的大偏差性质的分析。提案的第二部分讨论了为所谓的“资源系统的交互用户”开发随机过程模型。这些模型描述了存在有限资源集的大量用户的情况。经济、金融和交通领域都有这样的例子。这项工作的目标是发展模型、极限定理和模型简化。本研究分为两个部分。第一部分从大偏差理论的角度思考问题。这一理论试图估计和刻画随机系统中的罕见事件。这种罕见的事件可能在决定许多由随机过程建模的系统的性能方面发挥关键作用。一个令人感兴趣的问题是对排队系统的大偏差性质的分析，特别是对通信系统中出现的那些性质的分析。同时，大偏差理论在高速网络(包括ATM网络)的分析和设计中具有很大的潜力。工作的重点是扩展一些最近开发的方法，这些方法可以处理这类困难的问题。研究的第二部分涉及为我们所说的“资源系统的交互用户”开发随机过程模型。这些模型描述了存在有限资源集的大量用户的情况。经济、金融和交通领域都有这样的例子。需要这样的动态模型来预测用户群体将如何适应环境的变化。这部分提案的主要目标是模型的发展和模型的简化。