Stochastic comparability and dual Q-functions

In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller-Reuter-Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density cl-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given. (C) 1999 Academic Press.