Remarks on suprema of Lévy processes with light tailes

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Abstract

Let X(t),0≤t≤1 be a Lévy process. A comparison between the right tail of sup0≤t≤1X(t) and the right tail of X(1) is considered. An example is given for which these tailes are incomparable. A class of Lévy process with "light" tails is described for which these tails have the same behavior.

Original languageEnglish
Pages (from-to)41-48
Number of pages8
JournalStatistics and Probability Letters
Volume43
Issue number1
DOIs
StatePublished - 15 May 1999

Keywords

  • 60G70
  • Compound Poisson process
  • Lévy process
  • Primary 60G17
  • Secondary 60E07
  • Tail behavior

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