MEAN FIRST-PASSAGE TIMES FOR SYSTEMS DRIVEN BY EQUILIBRIUM PERSISTENT-PERIODIC DICHOTOMOUS NOISE

In a recent paper, [J. M. Porra, J. Masoliver, and K. Lindenberg, Phys . Rev. E 48, 951 (1993)], we derived the equations for the mean first- passage time for systems driven by the coin-toss square wave, a partic ular type of dichotomous noisy signal, to reach either one of two boun daries. The coin-toss square wave, which we here call periodic-persist ent dichotomous noise, is a random signal that can only change its val ue at specified time points, where it changes its value with probabili ty q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals tau. Here we consider the stationary version of this signal, that is, ''equilibrium'' periodic-p ersistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuiti es or the oscillations found in the case of nonstationary noise. We al so discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.