Limit theorems for renewal processes with infinite mean interarrival time under random inspection

Statistics & Probability Letters, vol. 227, pp. 110527

Abstract

Analogues to fundamental asymptotic relations in renewal theory are considered under the assumption that the time is a random variable and that the interarrival times have infinite mean. Limits are given for interarrival times with regularly varying tail and for sequences of parameters of the respective random-time distribution under mild conditions. An application to alternating renewal processes is shown.

Authors 1

1. Diana Rauwolf corresponding Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics, RWTH Aachen University, Aachen, D-52056, Germany