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Risk sensitive control of Markov processes in countable state space. (English) Zbl 0866.93101
Summary: We consider infinite horizon risk-sensitive control of Markov processes with discrete-time and denumerable state space. This problem is solved by proving, under suitable conditions, that there exists a bounded solution to the dynamic programming equation. The dynamic programming equation is transformed into an Isaacs equation for a stochastic game, and the vanishing discount method is used to study its solution. In addition, we prove that the existence conditions are also necessary.

93E20 Optimal stochastic control
91A60 Probabilistic games; gambling
Full Text: DOI
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