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Abstract

We consider discrete time partially observed ergodic control problem of Markov process $(x_n)$ in the case when the only available observation is of the form $y_n=h(x_n)$, where $h$ is a deterministic function. The problem is first solved in the case when the observation space is at most countable and then it is generalized, although in general case we don't have explicit form for the transition operator of associated filtering process. In the talk some results of an old paper of L. Stettner, Appl. Math. 22,1 (1993), 25--38, are used intensively.