Abstract
We consider the age processes A(1)≥⋯≥A(n) associated to a monotone sequence R(1)⊆⋯⊆R(n) of regenerative sets. We obtain limit theorems in distribution for (A_t^{(1)},\ldots, A_t^{(n)})andfor((1/t) A_t^{(1)},\ldots,(1/t)A_t^{(n)})$, which correspond to multivariate versions of the renewal theorem and of the Dynkin–Lamperti theorem, respectively. Dirichlet distributions play a key role in the latter.