Kramers escape driven by fractional Brownian motion

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.

14 pages, 16 figures, RevTeX4

References in corpus (7)

• First-passage times in complex scale-invariant media
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Quantitative analysis of single particle trajectories: mean maximal excursion method
• Anomalous diffusion in correlated continuous time random walks
• Single-File diffusion in a Box
• Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance
• Generalized Langevin Equation Formulation for Anomalous Polymer Dynamics

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