A comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the intricate measure-theoretic issues. Establishes the most general possible theory of finite and infinite horizon stochastic dynamic programming models, through the use of analytic sets and universally measurable policies. Develops general frameworks for dynamic programming based on abstract contraction and monotone mappings.
Bertsekas, Dimitri P., and Steven E. Shreve. Stochastic optimal control: the discrete-time case. Vol. 5. Athena Scientific, 1996.