## 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 language | English |
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Pages (from-to) | 8-17 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 330 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Dec 2003 |

Event | Randomes and Complexity - Eilat, Israel Duration: 5 Jan 2003 → 9 Jan 2003 |

## Keywords

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