Kramers escape driven by fractional Brownian motion

TL;DR

This paper studies how fractional Gaussian noise influences the escape times of particles from a potential well, revealing different behaviors in subdiffusive and superdiffusive regimes through numerical and analytical methods.

Contribution

It provides new insights into the dependence of escape times on the Hurst exponent and diffusivity in fractional Brownian motion-driven systems.

Findings

Escape times follow an exponential distribution.

Escape becomes faster as the Hurst exponent decreases.

Analytical calculations support numerical observations.

Abstract

We investigate the Kramers escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time as function of H and the particle diffusivity D. We observe different behavior for the subdiffusive (antipersistent) and superdiffusive (persistent) domains. In particular we find that the escape becomes increasingly faster for decreasing values of H, consistent with previous findings on the first passage behavior. Approximate analytical calculations are shown to support the numerically observed dependencies.