First passage times distribution dependence on noise statistics and colour in a simple dynamical system

Abstract

The effect of changing noise statistics on first passage times (FPT) distribution is studied by means of digital simulation in a simple dynamical system. The first experimental determination of the FPT distribution is given in three different situations, involving “shot”, dichotomic and gaussian noise statistics. In the first two cases, the experimental results are compared with an exact theory recently developed by Lindenberg et al., whilst the results obtained with gaussian noise statistics are compared with the theoretical prevision of Doering et al. A remarkably good agreement between theory and experiment is found. Important effects on the FPT distribution are found by increasing the correlation time τ c of the noise.