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.

首席研究员将在可交换性的一般领域内继续他的工作。他的广泛兴趣涵盖了概率论的各个方面，从基本的基础和表示定理，通过交换过程的特定性质，到各种应用和扩展到概率论的其他领域。本文主要讨论了多元表示定理及其与多重随机积分的关系、可扩展性或子序列不变性的概念、稳定随机积分的表示和可交换区间划分的性质、它们的局部时间随机测度和Palm分布。