Mathematical Sciences: Probability in Banach Spaces and Diffusion Processes

数学科学：Banach 空间和扩散过程中的概率

• 批准号: 8902418
• 负责人: Joel Zinn
• 金额: $ 21.75万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902418&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Probability; Banach; Spaces

The principal investigators will continue their work in various areas of probability theory. One investigator will continue his study of limit theorems for empirical measures. This has both direct and indirect applications to statistics, and in particular to the bootstrap technique of estimation. A second investigator will study the relationship between Gaussian and Markov processes. Each of these processes acts as a model of many natural phenomena, but each makes different assumptions. A third investigator will continue his study of diffusion processes which involve discontinuity or singularity of the coefficients of the process, the state space, or the boundary. This study has indirect applications to stochastic control. ***

主要研究人员将继续他们在概率论各个领域的工作。一位研究者将继续他对经验测度的极限定理的研究。这对统计学有直接和间接的应用，特别是对自举估计技术。第二名研究员将研究高斯过程和马尔可夫过程之间的关系。这些过程中的每一个都是许多自然现象的模型，但每一个都有不同的假设。第三位研究者将继续研究涉及过程、状态空间或边界系数的不连续或奇异的扩散过程。本研究对随机控制有间接应用。＊＊＊