Finite Approximations in Discrete-Time Stochastic Control

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for