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On the extreme flights of one-sided Lévy processes

✍ Scribed by Iddo Eliazar; Joseph Klafter

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
223 KB
Volume
330
Category
Article
ISSN
0378-4371

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✦ Synopsis

We explore the statistical behavior of the order statistics of the ights of one-sided LÃ evy processes (OLPs). We begin with the study of the extreme ights of general OLPs, and then focus on the class of selfsimilar processes, investigating the following issues: (i) the inner hierarchy of the extreme ights-for example: how big is the 7th largest ight relative to the 2nd largest one?; and, (ii) the relative contribution of the extreme ights to the entire ' ight aggregate'-for example: how big is the 3rd largest ight 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 ight tails (which is far larger than the selfsimilar class).

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