On tails of exit times of multidimensional L\'evy processes

TL;DR

This paper proves that the exit times of any non-constant multidimensional Lévy process from a ball have exponentially light tails, using a simple argument based on independence of increments and geometric considerations.

Contribution

It introduces a straightforward proof that the exit times of multidimensional Lévy processes have exponentially light tails, expanding understanding of their probabilistic behavior.

Findings

Exit times have exponentially light tails

The proof relies on independence of increments and geometric properties of R^d

Applicable to all non-constant Lévy processes in R^d

Abstract

Using a very simple argument based on the indepenence of increments and the fact that in a finite dimensional space $R^{d}$ there are not too many directions, we derive a theorem stating that exit time of any (non-constant) L\'{e}vy process on $R^{d}$ from a ball has exponentially light tails.