Mathematical Sciences: Brownian Motion & Random Partitions

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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.