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.
Hee, van, K. M., & Wessels, J. (1978). Markov decision processes and strongly excessive functions. Stochastic Processes and their Applications, 8(1), 59-76. https://doi.org/10.1016/0304-4149(78)90067-4