Occupation times of alternating renewal processes with Lévy applications

Nicos Starreveld, Réne Bekker, Michel Mandjes

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper we present a set of results relating to the occupation time α(t) of a process X(·). The first set of results concerns exact characterizations of α(t), e.g. in terms of its transform up to an exponentially distributed epoch. In addition, we establish a central limit theorem (entailing that a centered and normalized version of α(t)/t converges to a zero-mean normal random variable as t→∞) and the tail asymptotics of P(α(t)/t≥q). We apply our findings to spectrally positive Lévy processes reflected at the infimum and establish various new occupation time results for the corresponding model.

Original languageEnglish
Pages (from-to)1287-1308
Number of pages22
JournalJournal of Applied Probability
Volume55
Issue number4
DOIs
Publication statusPublished - Dec 2018

Bibliographical note

Published online: 16 January 2019

Keywords

  • alternating renewal process
  • central limit theorem
  • large deviations
  • Lévy process
  • Occupation time
  • reflected Brownian motion

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