Mathematical Sciences: Research Problems in Stochastic Control and Numerical Approximation

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The following topics will be investigated: (1) Some Singular Stochastic Control Problems: Two problems: One is concerned with the analysis of a class of singular control problems in several dimensions, and the second pertains to a adapted version of singular stochastic control in one dimension. (2) Impulse Control Problems: Two novel applications of impulse control theory to optimal maintenance and sequential scheduling problems will be studied. (3) Ergodic Control Problems with a class of stochastic control of diffusion with jumps with a long- term average criterion. The emphasis is on the study of the associated invariant measure. (4) Numerical Analysis of Stochastic Control Problems: Numerical algorithm for solving a class of singular control problems in several dimensions. Numerical approximation of some Hamilton-Jacobi-Bellman equations. (5) Some Problems in Stochastic Distributed- Parameter Sytems: The investigators plan to study the solution of an infinite-dimensional H.J.B. equation arising from optimal control of a non-linear stochastic distributed system. The stability and asymptotic behavior of such a system with possible degeneracy will be investigated. This research is part of control theory with potential applications in engineering and computer science.