Alsmeyer, G. The Markov renewal theorem and related results. (English) Zbl 0906.60052 Markov Process. Relat. Fields 3, No. 1, 103-127 (1997). Summary: We give a new probabilistic proof of the Markov renewal theorem for Markov random walks with positive drift and Harris recurrent driving chain. It forms an alternative to the one recently given by the author [Stochastic Processes Appl. 50, No. 1, 37-56 (1994; Zbl 0789.60066)] and follows more closely the probabilistic proofs provided for Blackwell’s theorem in the literature by making use of ladder variables, the stationary Markov delay distribution and a coupling argument. A major advantage is that the arguments can be refined to yield convergence rate results. Cited in 1 ReviewCited in 8 Documents MSC: 60J05 Discrete-time Markov processes on general state spaces 60G50 Sums of independent random variables; random walks 60K05 Renewal theory 60K15 Markov renewal processes, semi-Markov processes Keywords:Markov random walks; ladder variables; Harris recurrence; regeneration epochs; coupling; cyclic decomposition PDF BibTeX XML Cite \textit{G. Alsmeyer}, Markov Process. Relat. Fields 3, No. 1, 103--127 (1997; Zbl 0906.60052)