A Fixed Point Approach to Solve the Average Cost Optimality Equation for Semi-Markov Decision Processes with Feller Transition Probabilities

Abstract

Semi-Markov control processes with Feller (also known as weakly continuous) transition probabilities and unbounded cost functions are considered. We give sufficient conditions for the existence of a lower semicontinuous and continuous solutions to the average cost optimality equation. The proof is based on a fixed point argument.

Keywords:

• Average cost optimality equation
• Borel state space
• Semi-Markov decision process

Mathematics Subject Classification:

• Primary 90C40
• Secondary 90C93

Acknowledgments

The author wishes to thank Professor Andrzej S. Nowak for helpful discussions. Thanks are also due to the referee for several suggestions made to improve the presentation.

This research was partially supported by MEiN Grant 1 P03A 01030.