Mathematical Sciences: Research on Optimal Stochastic Control and Nonlinear Estimation

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This research is part of an on-going program by the principal investigator and associates. Topics in the following areas are to be considered: (1) controlled Markov diffusions and nonlinear PDEs; (2) asymptotic properties of nearly deterministic Markov processes; (3) financial economics applications; (4) singular stochastic control; (5) computational methods in stochastic control; (6) stochastic calculus of variations; (7) nonlinear estimation. Analytical methods based on viscosity solution techniques for nonlinear differential equations as well as probabilistic methods will be studied. These theoretical studies are the basis for applied problems ranging from decisions at the stock market level to the control of spaceships.