Markov chains with stationary transition probabilities 
Kai Lai Chung
Springer
From the reviews:  <p>  J. Neveu, 1962 in Zentralblatt fГјr Mathematik, 92.Band Heft 2, p. 343:  "Ce livre Г©crit par l'un des plus Г©minents spГ©cialistes en la matiГЁre, est un exposГ© trГЁs dГ©taillГ© de la thГ©orie des processus de Markov dГ©finis sur un espace dГ©nombrable d'Г©tats et homogГЁnes dans le temps (chaines stationnaires de Markov)."<p>  N.Jain, 2008 in Selected Works of Kai Lai Chung, edited by Farid AitSahlia (University of Florida, USA), Elton Hsu (Northwestern University, USA), & Ruth Williams (University of California-San Diego, USA), Chapter 1, p. 15: "This monograph deals with countable state Markov chains in both discrete time (Part I) and continuous time (Part II). [...] Much of Kai Lai's fundamental work in the field is included in this monograph.  Here, for the first time, Kai Lai gave a systematic exposition of the subject which includes classification of states, ratio ergodic theorems, and limit theorems for functionals of the chain."<p>