On Algebraic and Exponential Transience for Continuous-Time Markov Chains

In this paper, we investigate algebraic and exponential transience for continuous-time Markov chains (CTMCs). Equivalent relations of these transience are revealed between CTMCs and their jump chains and dual processes. The results are further applied to derive the criteria of these transience for general CTMCs, generalized Markov branching processes and birth-death processes.