Mathematical Sciences: Brownian Motion & Random Partitions

皮特曼 研究人员计划继续目前的研究线到随机过程，特别是布朗运动，随机分区，以及相关的过程。 特别提出的主题研究如下：随机分区结构与从属，两个参数推广的Ewens'随机分区结构和它的关系的游览理论的布朗运动和贝塞尔过程，随机缩放操作的道路上的布朗运动和贝塞尔过程，和各种subfiltrations的布朗过滤。 调查员将继续目前的研究线到随机过程，特别是布朗运动，随机分区，以及相关的过程。 随机划分可以应用于组合学、物理学和遗传学。 这些模型是有用的，在研究随机现象，涉及聚类或聚合在各种各样的情况下。 这是对随机过程的数学结构的基础研究。 这方面的进展提高了我们对这些过程的理解，并有可能在许多知识领域的应用。

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.