This paper considers the average optimality for a continuous-time Markov decision process in Borel state and action spaces, and with an arbitrarily unbounded nonnegative cost rate. The existence of a deterministic stationary optimal policy is proved under the conditions that allow the following; the controlled process can be explosive, the transition rates are weakly continuous, and the multifunction defining the admissible action spaces can be neither compact-valued nor upper semicontinuous.
"Average optimality for continuous-time Markov decision processes under weak continuity conditions." J. Appl. Probab. 51 (4) 954 - 970, December 2014.