Mathematical Sciences: Research in Stochastic Process Theory

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The principal investigator will conduct research in three areas of the theory of stochastic processes and related partial differential equations. The first area is concerned with proving the large deviation principle for Markov stochastic processes with "discontinuous statistics," a class that includes diffusions with discontinuous drift and small diffusion coefficient as well as certain scaled queueing systems. The second area considers the problem of obtaining the full asymptotic expansion for certain important classes of jump Markov processes. The last part of the proposed work involves research in the area of numerical methods for continuous time stochastic control problems. The principal investigator will conduct research on several problems that are at the interface of stochastic processes, a branch of probability theory, and stochastic control, a branch of applied mathematics. The problems are motivated by issues involved with understanding systems of queues, which arise naturally in several applications, for example communications.