Superposed continuous renewal processes A Markov renewal approach

Lam and Lehoczky (1991) have recently given a number of extensions of classical renewal theorems to superpositions of p independent renewal processes. In this article we want to advertise an approach that more explicitly uses a Markov renewal theoretic framework and thus leads to a simplified derivation of their main results together with a number of new ones. Those include a Stone-type decomposition for the resulting Markov renewal measure and a number of convergence rate results which extend the corresponding results for single renewal processes.