Mathematical Sciences: Study of Measure-Valued Processes

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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.