Mathematical Sciences: Probability: Symmetries and Local Structure

数学科学：概率：对称性和局部结构

• 批准号: 9303050
• 负责人: Olav Kallenberg
• 金额: $ 6万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303050&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Probability; Symmetries; Local

The investigator intends to continue his research in various areas of probability theory that are closely related to his previous work. In particular, he is planning to study certain characterization problems in multivariate exchangeability theory, where the representations may be expressed as sums of multiple Wiener-Ito integrals on tensor products of suitable Hilbert spaces. He will further extend his earlier study of exchangeable random sets, their Palm measures and local properties. In both of these general areas, there are many related problems of a more foundational nature that will also be addressed. The investigator will continue his research on certain basic structural problems in probability theory. This research will provide the general conceptual framework and basic theory necessary for work of other researchers in more applied fields, such as statistics and statistical mechanics, which in turn are useful for technology and other areas of science.

研究者打算继续在与他之前的工作密切相关的概率论各个领域进行研究。 特别是，他计划研究多元可交换性理论中的某些表征问题，其中的表示可以表示为合适希尔伯特空间的张量积上的多个维纳-伊托积分的和。 他将进一步扩展他早期对可交换随机集、它们的 Palm 度量和局部属性的研究。 在这两个一般领域中，还有许多更基础的相关问题也将得到解决。 研究者将继续研究概率论中的某些基本结构问题。 这项研究将为统计和统计力学等更多应用领域的其他研究人员的工作提供必要的一般概念框架和基础理论，而这反过来又对技术和其他科学领域有用。