Mathematical Sciences: Study of Measure-Valued Processes

本研究涉及随机测量值过程研究中的几个问题，这些过程模拟了大人口的空间分布和时间发展。这些问题涉及到这些过程的一般公式，以及它们通过德菲内蒂定理与相互作用粒子的可交换系统的联系。本研究研究群体遗传学中出现的过程。特别是，这项工作涉及研究群体遗传学中使用的特定模型的概括，并确定它们与相互作用的粒子系统的联系。

This research involves several problems in the study of stochastic measure-valued processes, processes which model the spatial distribution and time development of a large population. The problems are concerned with the general formulation of these processes and with their connection, via de Finetti's theorem, with exchangeable systems of interacting particles. This research studies processes which arise in population genetics. In particular, the work involves studying generalizations of the specific models used in population genetics and identifying their connections to interacting particles systems.