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Discounted Markov control processes induced by deterministic systems. (English) Zbl 1249.90312
Summary: This paper deals with Markov control processes (MCPs) on Euclidean spaces with an infinite horizon and a discounted total cost. Firstly, MCPs which result from deterministic controlled systems are analyzed. For such MCPs, conditions that permit to establish the equation known in the economics literature as Euler’s equation (EE) is given. An example of a MCP with a deterministic controlled system is presented, where in order to obtain the optimal value function, EE is applied to the value iteration algorithm. Secondly, the MCPs which result from the perturbation of deterministic controlled systems with a random noise are dealt with. The conditions which allow to obtain the optimal value function and the optimal policy of a perturbed controlled system are presented, in terms of the optimal value function and the optimal policy of the corresponding deterministic controlled system. Finally, several examples to illustrate the last case mentioned are presented.

MSC:
90C40 Markov and semi-Markov decision processes
93E20 Optimal stochastic control
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