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Average optimality for risk-sensitive control with general state space. (English) Zbl 1128.93056
A discrete-time Markov control process on a general state space is considered. The aim of the paper is to establish the optimality inequality for risk-sensitive dynamic programming and derive an optimal stationary policy. A similar result was obtained by Hernández-Hernández and Marcus under the assumption that there exists a stationary policy which induces a finite average cost that is equal some constant in each state. Here, instead of this assumption, the author assumes that a certain family of functions is bounded which makes the process reach “good states” sufficiently fast.
For related papers see: [D. Hernández-Hernández and S. I. Marcus, Appl. Math. Optim. 40, 273–285 (1999; Zbl 0937.90115)].

##### MSC:
 93E20 Optimal stochastic control 60J05 Discrete-time Markov processes on general state spaces 91A15 Stochastic games, stochastic differential games
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