Geodesic
Optimization of Discrete-Time, Stochastic Systems
Serdica Mathematical Journal, Tome 21 (1995) no. 4, pp. 267-282.

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In this paper we study discrete-time, finite horizon stochastic systems with multivalued dynamics and obtain a necessary and sufficient condition for optimality using the dynamic programming method. Then we examine a nonlinear stochastic discrete-time system with feedback control constraints and for it, we derive a necessary and sufficient condition for optimality which we then use to establish the existence of an optimal policy.
Keywords: Bellman Function, Dynamic Programming, Conditional Expectation, Measurable Selection, Induction 
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     author = {Papageorgiou, Nikolaos},
     title = {Optimization of {Discrete-Time,} {Stochastic} {Systems}},
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Papageorgiou, Nikolaos. Optimization of Discrete-Time, Stochastic Systems. Serdica Mathematical Journal, Tome 21 (1995) no. 4, pp. 267-282. http://geodesic.mathdoc.fr/item/SMJ2_1995_21_4_a0/