Two cross-correlated dichotomic noises: Barrier crossing problem

Escape of an overdamped particle driven by two correlated dichotomic noises (DN) from a triangle potential well is studied. A general description of statistical properties of the noises is developed in terms of master equation and correlation functions. Using the kinetics of these noises, an equation for the mean first-passage times can be deduced, which enables us to investigate the impact of non-zero covariance on the barrier crossing rate. In various cases, both the acceleration and the slowing down of the escape process can be observed.