Rare Events in the Presence of Heavy Tails

Abstract

We consider random walks and queues where one or more of the underlying distributions are heavy-tailed, more precisely subexponential (e.g., the tails are regularly varying, DFR Weibull type or lognormal type). This contrast the standard light-tailed assumptions (for example in large deviations theory) where exponential moments are required. The problem is to derive asymptotic expressions for rare events like large random walk maxima or large cycle maxima, large waiting times or large sojourn time in a network, or excursions above a large level, and also to study the behaviour of the process leading to the occurence of the rare event. The results support the folklore that in the heavy-tailed case, rare events occur as consequence of one big jumpKeywordsRandom WalkRare EventHeavy TailExtremal IndexJackson NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.