Controlled semi-Markov models under long-run average rewards

Let the state space S be a Borel subset of a complete separable metric space, the action space A compact metric. Existence of stationary optimal policies is proved and a dynamic programming equation derived for general semi-Markov models under the long-run average reward criterion, focusing on it as a limiting case of optimization under discounting as the discount factor goes to one. This extends many earlier results. An example of Reed (1974) on harvesting a natural resource provides an application not covered by earlier results.