Sufficiency of stationary policies for constrained continuous-time Markov decision processes with total cost criteria

This paper, based on the compactness-continuity and finite value conditions, establishes the sufficiency of the class of stationary policies out of the general class of history-dependent ones for a constrained continuous-time Markov decision process in Borel state and action spaces with total nonnegative cost criteria. The controlled process is not necessarily absorbing, the discount factor can be identically equal to zero, and the transition rates can also be equal to zero, which account for the major technical difficulties. Models with these features seemingly had not been handled in the previous literature.