Extremes of Levy processes with light tails

TL;DR

This paper establishes conditions where the probability that a Levy process with light tails exceeds a certain level during a unit interval is asymptotically equivalent to the probability that its endpoint exceeds that level.

Contribution

It provides new criteria linking the tail behavior of Levy processes to their supremum over a fixed interval, enhancing understanding of their extreme value properties.

Findings

Tail probability of supremum is equivalent to endpoint tail under certain conditions

Conditions for light-tailed Levy processes to have specific extremal behavior

Theoretical characterization of Levy process extremes with light tails

Abstract

We give conditions under which the tail probability of the supremum over unit interval of a Levy process with light tail is equivalent to the tail of the value of the process at the right endpoint.