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Controlled diffusion processes

Vivek S. Borkar, School of Technology and Computer Science, Tata Institute of Fundamental Researc


Abstract
This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Several other related topics are briefly sketched.

AMS 2000 subject classifications: Primary 93E20; secondary 60H30.

Keywords: controlled diffusions, optimal control, dynamic programming, Hamilton-Jacobi-Bellman equations, partial observations.

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Borkar, Vivek S., Controlled diffusion processes, Probability Surveys, 2, (2005), 213-244 (electronic).

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