On the Tail Behaviour of Record-Time Distributions in a Random Record Process

Abstract

Consider a sequence of independent and identically distributed random variables attached to the points of an independent point process $P$. The random record process is the epochs of successive maxima in this sequence. In this paper necessary and sufficient conditions are found to ensure a certain tail behaviour for the distributions of times to successive records, and interrecord times, when $P$ is a renewal process with relatively stable partial sums for its intervals.