Resonant behavior of a Poisson process driven by a periodic signal

Abstract

The statistical properties of the residence times of a periodically modulated Poisson process (time-dependent shot noise) on a line segment are analyzed. They show the characteristic features of a resonant behavior, which is similar in many aspects to the stochastic resonance taking place in systems confined in monostable or multistable potentials. The dependence of the mean residence time on both the frequency of the periodic stimulus and its amplitude is studied in detail. The behavior of this parameter also displays the effects associated with the interplay between noise and deterministic modulation.