The hierarchy of exit times of Levy-driven Langevin equations

In this paper we consider the first exit problem of an over-damped Levy driven particle in a confining potential. We survey results obtained in recent years from our work on the Kramers' times for dynamical systems of this type with Levy perturbations containing heavy, and exponentially light jumps, and compare them to the well known case of dynamical systems with Gaussian perturbations. It turns out that exits induced by Levy processes with jumps are always essentially faster than Gaussian exits.