Mathematical Sciences: Topics in Markov Processes

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The investigator will continue his work in the general area of Markov processes. Recently, the investigator with a collaborator developed a set of invertible transformations of a Markov process which preserved the collection of excessive functions of the process. This collection is a symmetry group which can be used to construct Markov functions, which when composed with Markov processes result in a new Markov process (if the speed is corrected). The investigator will continue to study the probabilistic structure of the Markov process which is coded in the algebraic structure of the group. This study will yield a new algebraic technique for analyzing the structure of Markov processes. The investigator will continue his work in the general area of Markov processes. A Markov process is a probabilistic model which is characterized by the statement that in order to characterize the future of the process, it is enough to know the current state (and not the past) of the process. This model has been used successfully in fields as diverse as economics to chemistry and physics. The investigator will be studying the structure of such processes by using a different branch of mathematics, i.e. algebra.