Escape process in systems characterised by stable noises and position-dependent resting times

TL;DR

This paper investigates the escape process in systems driven by stable noises with position-dependent resting times, analyzing how medium heterogeneity influences first passage times and escape rates in both one and two dimensions.

Contribution

It introduces a model with position-dependent waiting times and stochastic dynamics formulated via subordination, highlighting differences from Gaussian cases and Levy flights.

Findings

Escape rate depends on stability index and memory parameter.

Medium heterogeneity significantly affects first passage time distributions.

Distinct behaviors observed between Gaussian and Levy flight scenarios.

Abstract

Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed to the underlying self-similar structure. Both one and two dimensional case are analysed. The random walk description involves a position-dependent waiting time distribution. On the other hand, the stochastic dynamics is formulated in terms of the subordination technique where the random time generator is position-dependent. The first passage time problem is addressed by evaluating a first passage time density distribution and an escape rate. The influence of the medium nonhomogeneity on those quantities is demonstrated; moreover, the dependence of the escape rate on the stability index and the memory parameter is evaluated. Results indicate essential differences between the Gaussian case and the case involving Levy flights.