The Markov Renewal Theorem and Related Results
Institut f¨ur Mathematische Statistik
Westf¨alische Wilhelms-Universit¨at M¨unster
D-48149 M¨unster, Germany
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 in  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.
AMS 1991 subject classifications. 60J05, 60J15, 60K05, 60K15.
Keywords and phrases. Markov random walks, ladder variables, Harris recurrence, regeneration epochs,