On the use of Lyapunov methods in renewal theory
Let \(N\) denote the random measure with atoms at \(T_n, n\in N\), where \(0<T_1<T_2\dots\) are points of a renewal process. The aim of the paper is the study of the asymptotic behaviour of processes associated with \(N\), in particular, the age process \(\{A_t, t\geq 0 \}\) which is defined as the distance between \(t\) and the first atom of \(N\) before \(t\). Convergence of moments and exponential moments of \(A_t\) to the corresponding stationary moments is proved under suitable conditions, and rates of convergence are studied. Also, rates of convergence for Blackwell's theorem are established.
scientific article; zbMATH DE number 1554279
scientific article