Mathematical Sciences: Exchangeability Theory and its Ramifications

数学科学：可交换性理论及其影响

• 批准号: 9002732
• 负责人: Olav Kallenberg
• 金额: $ 8.03万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002732&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Exchangeability; Theory; its

The principal investigator will continue his work within the general area of exchangeability. His general interest ranges over all aspects of the theory, from the basic foundations and representation theorems, via specific properties of exchangeable processes, to a variety of applications and extension to other areas of probability theory. The present proposal is focused on some specific problems involving multivariate representation theorems and their relation to multiple stochastic integration, the notion of spreadability or subsequence invariance, the representation of stable stochastic integrals and properties of exchangeable interval partitions, their local time random measures and Palm distributions.

首席调查员将继续在交换性的一般领域继续他的工作。 他的一般兴趣在理论的各个方面范围从基本的基础和代表定理，通过可交换过程的特定属性到各种应用以及扩展到概率理论的其他领域。 本提案的重点是涉及多元表示定理的一些特定问题及其与多个随机整合的关系，可传播性或次序不变性的概念，稳定的随机积分的表示以及可交换间隔分区的属性，其本地时间随机测量和棕榈分布。