A computational analysis for mean exit time under non-Gaussian Lévy noises

Abstract

Complex dynamical systems are often subject to non-Gaussian random fluctuations. The exit phenomenon, i.e., escaping from a bounded domain in state space, is an impact of randomness on the evolution of these dynamical systems. The existing work is about asymptotic estimate on mean exit time when the noise intensity is sufficiently small. In the present paper, however, the authors analyze mean exit time for arbitrary noise intensity, via numerical investigation. The mean exit time for a dynamical system, driven by a non-Gaussian, discontinuous (with jumps), α-stable Lévy motion, is described by a differential equation with nonlocal interactions. A numerical approach for solving this nonlocal problem is proposed. A computational analysis is conducted to investigate the relative importance of jump measure, diffusion coefficient and non-Gaussianity in affecting mean exit time.