Uniform asymptotics for compound Poisson processes with regularly varying jumps and vanishing drift

Bart Kamphorst, Bert Zwart (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)

Abstract

This paper addresses heavy-tailed large-deviation estimates for the distribution tail of functionals of a class of spectrally one-sided Lévy processes. Our contribution is to show that these estimates remain valid in a near-critical regime. This complements recent similar results that have been obtained for the all-time supremum of such processes. Specifically, we consider local asymptotics of the all-time supremum, the supremum of the process until exiting [0,∞), the maximum jump until that time, and the time it takes until exiting [0,∞). The proofs rely, among other things, on properties of scale functions.

Original languageEnglish
Pages (from-to)572-603
Number of pages32
JournalStochastic Processes and their Applications
Volume129
Issue number2
DOIs
Publication statusPublished - 1 Feb 2019

Keywords

  • Compound Poisson process
  • First passage time
  • Heavy traffic
  • Large deviations
  • M/G/1 queue
  • Supremum
  • Uniform asymptotics

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