On the Extreme Flights of One-Sided Levy Processes

Abstract

We explore the statistical behavior of the order statistics of the flights of One-sided Levy 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).