Stochastic Control Problems and Numerical Methods

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The proposal deals with a large set of key problems in stochastic control and applications.Concerning Numerical Methods in Stochastic Control, the aim is to have a large set of effective algorithms which can be conveniently programmed, have good numerical properties, are robust, and for which there are convergence theorems under realistic conditions, so that numerical methods can fulfill their role as a practical and efficient approach to both investigation and design.The foundations are the Markov chain approximation methods. Algorithms with faster rate of convergence for the ergodic cost problem will be developed. The methods will be extended to stochastic differential games. This will allow treatment of robust and risk sensitive problems as well In many problems, the intensity of the noise is affected by the control. We will design practical and well performing algorithms. Numerical algorithms generally suppose that the drift terms are bounded.Problems with unbounded and controlled drift occur in communications theory and appropriate convergent algorithms will be developed. The treatment of ergodic costs with singular controls is one of the key remaining numerical problem areas, and is crucial in applications to communications theory and for heavy traffic limit models. Well performing algorithms will be developed. More generally, the theory of heavy traffic limits for the ergodic criteria and singular controls will be completed. We will also develop a complete theory of approximation methods for the modeling and control of Mobile communications systems when the channels are rapidly time varying in an arbitrary way. The heavy traffic models and associated limit theorems provide good guides for the analysis and control of a large variety of such systems.