M. Kus et K. Wodkiewicz, MEAN 1ST-PASSAGE TIME IN THE PRESENCE OF TELEGRAPH NOISE AND THE ORNSTEIN-UHLENBECK PROCESS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(6), 1993, pp. 4055-4063
We consider the problem of the escape time (mean first-passage time) f
rom a given interval in the case when the noise is a sum of many indep
endent random telegraph signals. We reduce the problem to the solution
of a linear system of algebraic equations valid for arbitrary intensi
ties and correlation times of the noise. The solution allows an easy i
nvestigation of the limiting case of the Ornstein-Uhlenbeck process. W
e find exact scaling laws obeyed by the mean first-passage times in th
e case of random telegraph signals and the Ornstein-Uhlenbeck process.