Asymptotic Results for Spectrally Positive Compound Poisson Processes

TL;DR

This paper investigates the asymptotic behavior of the lengths and heights of excursions of spectrally positive compound Poisson processes with negative drift, revealing strong dependence and scale symmetry.

Contribution

It provides new asymptotic relationships and insights into the dependence structure of excursion characteristics for spectrally positive compound Poisson processes.

Findings

Lengths and heights of excursions are asymptotically strongly dependent.

Excursion characteristics exhibit scale symmetry.

Results enhance understanding of process behavior during finite excursions.

Abstract

Finite excursions away from zero of a spectrally positive compound Poisson process with a negative drift can always be decomposed into two parts lying above and below zero, respectively. This paper is concerned with the asymptotic relationships among the lengths and heights of these two parts. Our results state that both their lengths and heights are asymptotically strongly dependent and exhibit a scale symmetry.