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的研究在概率论的各个领域是密切相关的，他以前的工作。 特别是，他正计划研究多元交换理论中的某些表征问题，其中的表示可以表示为合适的希尔伯特空间的张量积上的多个维纳-伊藤积分的总和。 他将进一步扩大他以前的研究可交换随机集，其棕榈措施和当地的财产。 在这两个一般性领域，还有许多更基本的相关问题也将得到处理。 研究者将继续他对概率论中某些基本结构问题的研究。 这项研究将提供一般的概念框架和基本理论，为其他研究人员在更多的应用领域，如统计和统计力学，这反过来又是有用的技术和其他科学领域的工作。