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.
- Stationary optimal policy
- dynamic programming equation
- uniformity in weak convergence
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics