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A fixed point approach to undiscounted Markov renewal programs. (English) Zbl 0558.90099

This paper shows how to use Brouwer’s fixed point theorem to prove the existence of a solution for the pair of optimality equations in Markov renewal programming. First models with a single communicating system are considered. Then the result is extended to the multichain case by decomposing the state space into a hieararchical structure of communicating systems.
Reviewer: M.Schäl

MSC:

90C40 Markov and semi-Markov decision processes
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