MEAN 1ST-PASSAGE TIME IN THE PRESENCE OF TELEGRAPH NOISE AND THE ORNSTEIN-UHLENBECK PROCESS

We consider the problem of the escape time (mean first-passage time) from a given interval in the case when the noise is a sum of many independent random telegraph signals. We reduce the problem to the solution of a linear system of algebraic equations valid for arbitrary intensities and correlation times of the noise. The solution allows an easy investigation of the limiting case of the Ornstein-Uhlenbeck process. We find exact scaling laws obeyed by the mean first-passage times in the case of random telegraph signals and the Ornstein-Uhlenbeck process.