Extremes of random variables observed in renewal times

TL;DR

This paper uses point process theory to analyze the asymptotic behavior of extreme values in renewal time observations, providing new insights into their distribution and extremal processes.

Contribution

It introduces a novel application of point process theory to characterize the asymptotic distribution of upper order statistics in renewal processes.

Findings

Derived limiting distributions for upper order statistics

Established asymptotic behavior of extremal processes

Provided theoretical framework for extremes in renewal times

Abstract

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.