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.

研究人员打算继续他在概率理论的各个领域的研究，这些研究与他以前的工作密切相关。 特别是，他计划在多元交换性理论中研究某些特征问题，在该理论中，这些表示形式可以表示为合适希尔伯特空间张量产品的多个Wiener-Ito积分的总和。 他将进一步扩展他对可交换随机组，棕榈措施和当地特性的早期研究。 在这两个一般领域中，都有许多相关的基本性质的问题也将被解决。 研究人员将继续他对概率理论中某些基本结构问题的研究。 这项研究将为其他研究人员（例如统计学和统计力学）的其他研究人员的工作提供一般概念框架和基本理论，这反过来又对技术和其他科学领域有用。