Mathematical Sciences: Topics in Stochastic Control and Random Media

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This proposal is concerned with the mathematical problems of stochastic control theory and multiple scattering of waves in random media. It is a product of joint efforts of two known specialists in this area, Professors Chow and Menaldi. The main research effort will be invested in the study of various theoretical issues in the stochastic control problems. It is assumed that dynamical process is subject to influence of random signals. The goal is to determine a control function that optimizes a certain objective, expressed as a function on process trajectories. The control is supposed to have an impulse character. This is an idealized version of a physical situation where one can observe abrupt changes inprocess trajectories, which can be thought of as discontinuities, or jumps. Fo example, the inventory stocks in a warehouse may be represented in this way, as they experience a jump in the value at the delivery of new stock. The control of an impulse nature is usually represented mathematically by Dirac distributions. The timings and masses of such impulses are the control parameters that one wants to select in an optimal fashion.