First Passage Time Statistics For Systems Driven by Long Range Gaussian Noises

Abstract

We examine the mean first passage time for a particle driven by highly correlated Gaussian fluctuations to reach one or more predetermined boundaries. We discuss a numerical algorithm to generate power-law correlated fluctuations and apply these to three physical examples. One is the arrival of a free particle at either end of an interval. The second is the decay of a particle from an unstable state. The third is the time for a particle to cross a barrier separating one well from another in a double well potential. In each case a comparison with the first passage time for a particle driven by Gaussian white noise is presented, as is an analysis of the dependence of the first passage time properties on the correlated noise parameters.