On the extreme flights of one-sided Lévy processes

Iddo Eliazar, Joseph Klafter

Research output: Contribution to journalConference articlepeer-review

Abstract

We explore the statistical behavior of the order statistics of the flights of one-sided Lévy processes (OLPs). We begin with the study of the extreme flights of general OLPs, and then focus on the class of selfsimilar processes, investigating the following issues: (i) the inner hierarchy of the extreme flights - for example: how big is the 7th largest flight relative to the 2nd largest one?; and, (ii) the relative contribution of the extreme flights to the entire 'flight aggregate' - for example: how big is the 3rd largest flight relative to the OLP's value? Furthermore, we show that all 'hierarchical' results obtained - but not the 'aggregate' results - are explicitly extendable to the class of OLPs with arbitrary power-law flight tails (which is far larger than the selfsimilar class).

Original languageEnglish
Pages (from-to)8-17
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Volume330
Issue number1-2
DOIs
StatePublished - 1 Dec 2003
EventRandomes and Complexity - Eilat, Israel
Duration: 5 Jan 20039 Jan 2003

Keywords

  • Extreme value theory
  • Fréchet distribution
  • Lévy flights
  • Order statistics
  • Selfsimilar Lévy processes

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