Dual and Feller–Reuter–Riley transition functions

In this paper, we investigate duality and Feller–Reuter–Riley (FRR) property of continuous-time Markov chains (CTMCs). A criterion of dual q-functions is given in terms of their q-matrices. For a dual q-matrix Q, a necessary and sufficient conditions for the minimal Q-function to be a FRR transition function are also given. Finally, by using dual technique, we give a criterion of FRR Q-functions when Q is monotone.