Research on Stochastic Systems and Filtering Theory and Applications

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The proposal covers four major areas in Stochastic Control. The first concerns singularly perturbed stochastic systems for both Ito and wide bandwidth noise driven systems, finite and infinite time problems, parametric singularities and approximations to the nonlinear filtering problems. The second concerns control, approximation and limit problems for queues and production systems in heavy traffic, and associated numerical methods. Special cases includes routing and singular control, control over an infinite time interval, numerical methods for scheduling under priorities, and the types of problems which occur in virtual circuit systems with many lines. The third area is that of efficient numerical algorithms, where reflected, singular, ergodic, constrained and heavy traffic problems will be emphasized, since there is relatively little available for these problems. The last class concerns some promising new approaches to the efficient and robust monte carlo optimization of parametrized controls of stochastic systems of high dimension, where the control is based on the actual observed data.