Mean first-passage time in the presence of colored noise: An exact theory

Abstract

We derive an exact solution for the mean first-passage time for an arbitrary one-dimensional system driven by the colored Ornstein-Uhlenbeck noise. We show that this exact solution can be systematically interpreted in terms of random telegraph signals. Using random telegraph signals as a tool we fully solve the difficult problem of non-Markovian boundary conditions associated with such a problem. The analytic solution with these boundary conditions give a complete solution of the escape time in the presence of colored noise.