Mathematical Sciences: Complex Stochastic Systems

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This award will support a research program in the areas of Markov processes, stochastic analysis, spatial point processes, chains with infinite memory, large deviation theory, branching processes, and stochastic control. Work on Markov processes will focus on processes constrained to a subset of their natural state space, measure-valued processes related to population genetics, and models of stochastic networks. A study of simulation and approximation methods for stochastic differential equations will emphasize asymptotics for the error in approximation. Work on large deviations will include both further theoretical developments and applications to simulation and hypothesis testing. Applications of branching processes to problems arising in fiber optic communication systems will be explored. Theoretical development for general stochastic control problems will include approximation methodology and existence theorems for Markov controls and optimal singular controls. Applications of stochastic control will focus on consumption models in the presence of mark imperfections. This award will support a research program in the areas of Markov processes, stochastic analysis, spatial point processes, and stochastic control. This research falls within the area of probability theory, but is motivated and will be applied to problems in a variety of fields: population genetics, engineering, and finance.