  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.
