Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed L\'evy noise

TL;DR

This paper investigates how small, heavy-tailed Lévy noise influences the time it takes for the Chafee-Infante equation to exit a stable state, providing insights into rare event dynamics under such stochastic perturbations.

Contribution

It offers a novel analysis of first exit times for the Chafee-Infante equation under small heavy-tailed Lévy noise, extending understanding of stochastic stability and exit phenomena.

Findings

Characterizes asymptotic behavior of exit times

Identifies impact of heavy-tailed noise on stability

Provides mathematical framework for rare event analysis

Abstract

We study the first exit times form a reduced domain of attraction of a stable fixed of the Chafee-Infante equation when perturbed by a heavy tailed L\'evy noise with small intensity.