The random record model

Abstract

This paper contains a detailed study of the random record model, which is the process of successive upper records in a sequence of independent and identically distributed variates occurring at the points of an independent point process. Asymptotic properties of the record and inter-record times, and of the number of records in a fixed interval, are derived, for both large time intervals and large record index numbers. A generalization which permits some dependence between the variates and the point process is also discussed, with emphasis on explicit results.