by Hou Zhenting (Central South University, P R China) , Li Junping (Central South University, P R China) , & Chen Anyue (University of LiverpoolUniversity of Hong Kong, UKHong Kong)

This book reports the recent progress in the field of continuous-time Markov chains (CTMCs), with a comprehensive and extensive discussion on its general theory and applications. It covers the properties of Q-matrix and transition function as well as the existence and uniqueness of Q-processes in stable and unstable cases. Monotonity, recurrency and ergodicity criteria are presented in this book. It also gives some important conclusions regarding the transiency properties, including invariant measures and quasi-limiting distributions for some important Q-processes.

• Transition Functions and Q-Matrix
• Some Basic Tools
• Existence of Q-Processes: Stable Q-Matrix Case
• Uniqueness of Q-Processes: Stable Q-Matrix Case
• Existence and Uniqueness: Unstable Q-Matrix Case
• Irreducibility and Recurrence
• Ergodicity and Equilibrium Distribution
• Absorbing Chains and Branching Processes
• Invariant Measure and Quasi-Limiting Distributions
• Reversibility and Birth-Death Processes
• Monotonity and Duality
• Coupling and Spectral Gap
• Markovian Queues and Skip-Free Processes