Collaborative Research: Ergodic Control of Stochastic Differential Equations Driven By a Class of Pure-Jump Levy Processes, and Applications to Stochastic Networks

合作研究：一类纯跳跃 Levy 过程驱动的随机微分方程的遍历控制及其在随机网络中的应用

基本信息

批准号：
1715210
负责人：
Ari Arapostathis
金额：
$ 21.1万
依托单位：
University of Texas at Austin
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-06-01 至 2021-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1715210&HistoricalAwards=false
关键词：
Collaborative Research Ergodic Control Stochastic

项目摘要

Queueing processes in large-scale networks are ubiquitous in society as exemplified by patient flow in hospitals, telephone call centers, service networks, and manufacturing and service operations management. This research will provide fundamental theoretical understanding of these queueing processes in the presence of batch arrivals. The results of this research will be put into direct applications to real-world stochastic networks through collaborations with the health systems and system analysis industry. This research will support under-represented minority groups and train young STEM graduates with new mathematical skills. This research concerns ergodic control problems for systems described by Ito stochastic differential equations (SDEs) driven by pure-jump Levy processes. The research objectives are: (1) to develop a comprehensive theoretical framework for ergodic control for a large class of controlled SDEs driven by a pure-jump Levy process; (2) to study a novel fully nonlinear problem that arises in admission control and falls outside the usual paradigm of stochastic control; and (3) to develop value iteration algorithms and spatial approximation methods in order to study large time asymptotics, and also to facilitate the numerical solution of the associated Hamilton-Jacobi-Bellman (HJB) equations, and the design of learning schemes for adaptive control in the presence of unknown parameters. This research will advance the basic science of applied mathematics and stochastic control, and make fundamental contributions to applied probability and stochastic networks.

大型网络中的排队过程在社会中无处不在，例如医院、电话呼叫中心、服务网络以及制造和服务运营管理中的患者流动。这项研究将为在批量到达的情况下这些排队过程提供基本的理论理解。这项研究的结果将通过与卫生系统和系统分析行业的合作，直接应用于现实世界的随机网络。这项研究将支持代表性不足的少数群体，并为年轻的 STEM 毕业生提供新的数学技能。本研究涉及由纯跳跃 Levy 过程驱动的伊藤随机微分方程 (SDE) 描述的系统的遍历控制问题。研究目标是：（1）为由纯跳跃 Levy 过程驱动的一大类受控 SDE 开发遍历控制的综合理论框架；（2）研究准入控制中出现的、不属于通常的随机控制范式的新型完全非线性问题； (3) 开发值迭代算法和空间逼近方法，以研究大时间渐进性，并促进相关的 Hamilton-Jacobi-Bellman (HJB) 方程的数值求解，以及自适应控制的学习方案的设计在存在未知参数的情况下。这项研究将推进应用数学和随机控制的基础科学，并对应用概率和随机网络做出基础性贡献。