Inertial L\'evy flights in bounded domains

TL;DR

This paper investigates the escape dynamics of inertial particles driven by Le9vy noise in bounded domains, analyzing mean first passage times, escape velocity, and energy, revealing their relation to properties of integrated Le9vy and Wiener processes.

Contribution

It provides a detailed analysis of escape kinetics for inertial Le9vy-driven particles, highlighting the connection to integrated Wiener processes and exploring sensitivity to initial conditions.

Findings

Mean first passage time relates to properties of integrated Le9vy and Wiener processes.

Escape velocity and energy are sensitive to initial conditions.

Properties of the escape process depend on the type of Le9vy noise and boundary conditions.

Abstract

The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by L\'evy noise from a bounded domain, restricted by two absorbing boundaries.Presence of two absorbing boundaries assures that the escape process can be characterized by the finite mean first passage time. The detailed analysis of escape kinetics shows that properties of the mean first passage time for the integrated Ornstein--Uhlenbeck process driven by L\'evy noise are closely related to properties of the integrated L\'evy motions which, in turn, are close to properties of the integrated Wiener process. The extensive studies of the mean first passage time were complemented by examination of the escape velocity and energy along with their sensitivity to initial conditions.