Mathematical Sciences: Brownian Motion & Random Partitions

皮特曼研究员计划继续目前对随机过程的研究，特别是布朗运动、随机分区和相关过程。提出的具体研究课题有：与从属子相关联的随机配分结构，evens随机配分结构的双参数推广及其与布朗运动和贝塞尔过程偏移理论的关系，布朗运动和贝塞尔过程路径上的随机缩放操作，以及布朗滤波的各种次滤波。研究者将继续研究随机过程，特别是布朗运动、随机分区和相关过程。随机分区可以应用于组合学、物理学和遗传学。这些模型在研究各种情况下涉及聚类或聚集的随机现象时非常有用。这是对随机过程数学结构的基础研究。这方面的进展增强了我们对这些过程的理解，并有可能应用于许多知识领域。

Pitman The investigator plans to continue present lines of research into stochastic processes, particularly Brownian motion, random partitions, and related processes. Particular subjects proposed for study are the following: random partition structures associated with a subordinator, the two parameter generalization of Ewens' random partition structure and its relation to the excursion theory of Brownian motion and Bessel processes, random scaling operations on the paths of Brownian motion and Bessel processes, and various subfiltrations of the Brownian filtration. The investigator will continue present lines of research into stochastic processes, particularly Brownian motion, random partitions, and related processes. Random partitions find applications to combinatorics, physics, and genetics. These models are useful in the study of random phenomena involving clustering or aggregation in a wide variety of contexts. This is fundamental research into the mathematical structure of stochastic processes. Progress in this direction enhances our understanding of these processes and has potential for application in numerous fields of knowledge.