Markov decision processes and strongly excessive functions

Strongly excessive functions play an important role in the theory of Markov decision processes and Markov games. In this paper the following question is investigated: What are the properties of Markov decision processes which possess a strongly excessive function? A probabilistic characterization is presented in the form of a random drift through a partitioned state space. For strongly excessive functions which have a positive lower bound a characterization is given in terms of the lifetime distribution of the process. Finally we give a characterization in terms of the spectral radius.