Renewal theory for embedded regenerative sets (Q1568297)

To a given regenerative set \({\mathcal R}\) on the real line one can associate a renewal process so that the increments of the latter correspond to the waiting times between successive occurrences of \({\mathcal R}\). One important object is the so-called age process and its limiting behaviour. The present paper is devoted to a multivariate extension of the model. The author considers a monotonically increasing sequence of \(n\) regenerative sets and the associated decreasing sequence of age processes. Limit theorems are obtained for the \(n\)-dimensional sequence of normalized age processes, as time tends to infinity.