Suprema of compound Poisson processes with light tails

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Abstract

It is known that if the Lévy measure of a Lévy process X(t), 0≤t≤1, is "heavy tailed", then the right tails of sup0≤t≤1X(t) and X(1) are of the same rate of decay. One of the results of this note is a description of a class of compound Poisson processes with negative drift and "light" tails (which is a subclass of Lévy processes) such that these tails are incomparable.

Original languageEnglish
Pages (from-to)145-156
Number of pages12
JournalStochastic Processes and their Applications
Volume90
Issue number1
DOIs
StatePublished - 1 Jan 2000

Keywords

  • Compound poisson process
  • Lévy process
  • Tail behavior

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