On finite state Markovian decision processes with compact decision sets

The paper deals with the problem of optimal control of a discrete time finite state Markovian decision process with the average cost criterion. The existence of stationary optimal policies is proved under the conditions that the decision sets are compact, reward functions are upper semi-continuous, transition functions continuously depend on decisions and one of the following assumptions is satisfied: 1) for any stationary policy there is only one ergodic class and the existence of transient states is allowed; 2) the sets of transition probabilities at any state contains a finite number of extremal points.