Superposed continuous renewal processes: A Markov renewal approach
Let \((S_n)_{n \geq 1}\) be the point process obtained as superposition of \(p \geq 2\) independent renewal processes. Though in general this process is no longer a renewal process, it shares the asymptotic properties of renewal processes as given in the renewal theorems. This has been shown by \textit{C. Y. T. Lam} and \textit{J. P. Lehoczky} [Adv. Appl. Probab. 23, No. 1, 64-85 (1991; Zbl 0723.60109)]. The author describes the superposition as a Markov renewal process and applies the Markov renewal theorems. This approach simplifies proofs and allows remarkable extensions. He states the generalized versions of the classical renewal theorems and, in case the increments of the basic renewal processes have spread out distributions, results on rates of convergence. As a prerequisite he proves a Stone-type decomposition for the Markov renewal measure of the superposition and uses the coupling technique.
scientific article; zbMATH DE number 894802
scientific article