Mathematical Sciences: Studies in Random Dynamical Systems

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The principal investigator will study three problems in random processes motivated by ideas from dynamical systems. In analogy with Hamiltonian systems, he will develop unified treatment of symmetry and diffusion. Borrowing from topological dynamics, he will develop the use of relative entropy for the study of stochastic processes - particularly those involving models for ion channels. Finally, from considerations in the dynamical theory of Brownian motion, he will develop a limit theorem to a stochastic partial differential equation modeling the motion of a white blood cell. The investigator will study three problems in random processes motivated by ideas from dynamical systems. His approach will use techniques from the fields of stochastic processes and geometric algebra. The models that he is considering are motivated by biological considerations, e.g. the motion of white blood cells.