Absorbing Continuous-Time Markov Decision Processes with Total Cost Criteria

Abstract

In this paper we study absorbing continuous-time Markov decision processes in Polish state spaces with unbounded transition and cost rates, and history-dependent policies. The performance measure is the expected total undiscounted costs. For the unconstrained problem, we show the existence of a deterministic stationary optimal policy, whereas, for the constrained problems withNconstraints, we show the existence of a mixed stationary optimal policy, where the mixture is over no more thanN+1 deterministic stationary policies. Furthermore, the strong duality result is obtained for the associated linear programs.