Drifted escape from the finite interval

TL;DR

This paper investigates how deterministic drift and symmetric alpha-stable noise influence the escape times of an overdamped particle from finite intervals, revealing universal patterns and conditions where noise diminishes drift effects.

Contribution

It introduces a universal pattern for mean first passage time based on the generalized Péclet number in drifted escape scenarios with alpha-stable noise.

Findings

Rescaled mean first passage time follows a universal pattern.

The Péclet number effectively discriminates between drift-dominated and noise-dominated regimes.

Alpha-stable noise can reduce the impact of drift even when drift is strong.

Abstract

Properties of the noise-driven escape kinetics are mainly determined by the stochastic component of the system dynamics. Nevertheless, the escape dynamics is also sensitive to deterministic forces. Here, we are exploring properties of the overdamped drifted escape from finite intervals under the action of symmetric $\alpha$-stable noises. We show that the properly rescaled mean first passage time follows the universal pattern as a function of the generalized P\'ecklet number, which can be used to efficiently discriminate between domains where drift or random force dominate. Stochastic driving of the $\alpha$-stable type is capable of diminishing the significance of the drift in the regime when the drift prevails.