Residence-time distributions as a measure for stochastic resonance

Stochastic resonance (SR) is believed to play an important role not only in numerous technological and physical applications, but also in biological and climate systems. Apart from spectral properties of the signal, residence-time distributions have been proposed as a measure for SR. For the paradigm of the motion of a periodically forced Brownian particle in a bistable potential, we explain the relation between first-passage-time and residence-time distributions. Going beyond exponential asymptotics, we are able to give rigorous expressions for the densities of these distributions. In a broad range of forcing frequencies and amplitudes, the distributions are found to be close to periodically modulated exponential ones, where the periodic modulations are governed by a universal function, depending on a single parameter related to the forcing period.

Joint work with Nils Berglund (CPT-CNRS Luminy, France).