Stochastic comparability and dual \(Q\)-functions (Q1301872)

The authors investigate the relationship between stochastic comparability, duality and Feller-Reuter-Riley transition functions that 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 \(q\)-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone \(q\)-functions is given in terms of \(q\)-matrix, as well.