On the active periods of nonlinear Shot Noise

We study the temporal ‘on-and-off’ structure of the recently introduced nonlinear Shot Noise model [I. Eliazar, J. Klafter, PNAS 102 (2005) 13779; I. Eliazar, J. Klafter, Nonlinear shot noise: Lévy, Noah, & Joseph, Physica A (2006), to appear], in which: (i) shots of random magnitudes ‘bombard’ a system stochastically in time; (ii) the magnitudes of ‘incoming’ shots decay to zero nonlinearly; and, (iii) the overall effect of the shots on the system is additive. When the shot-inflow and shot-decay satisfy certain conditions, the resulting Shot Noise alternates randomly between ‘active periods’ (in which the noise is ‘on’) and ‘silent periods’ (in which noise is ‘off’).