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Infinite horizon risk sensitive control of discrete time Markov processes with small risk. (English) Zbl 0977.93083
Summary: A control problem with risk sensitive ergodic performance criterion is considered for a discrete time Feller process. Using assumptions of uniform ergodicity and small risk factor, the existence and uniqueness of the solution to the Bellman equation is proved. Uniform approximations to such a solution in terms of discounted cost and discounted game problems are also shown.

MSC:
93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
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