On the extreme flights of one-sided Lévy processes

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 OLPʹs 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).