Mathematical Sciences: Exchangeability Theory and its Ramifications

首席调查员将继续在可互换性的一般领域内开展工作。他的主要兴趣涉及该理论的所有方面，从基本基础和表示定理，到可交换过程的特定性质，到概率论的各种应用和扩展到其他领域。本文主要讨论多元表示定理及其与多重随机积分的关系，可展开性或子序列不变性的概念，稳定随机积分的表示，可交换区间划分的性质，它们的局部时间随机度量和Palm分布。

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.