Abstract
We consider infinite horizon optimal control of Markov chains on complete metric spaces. We employ the overtaking optimality criterion, which is either applied to the expected cost-flow, or to the individual sample paths, yielding almost-sure optimality results. We use the existence of a solution pair (Φ(·), λ) to the optimality equation ℒΦ(x) = λ to establish and characterize optimal strategies. For finite state-spaces we derive sufficient, as well as necessary conditions for overtaking optimality.
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