Exact expressions have been found for the first two moments and the correlation function for an overdamped linear system subject to an external periodic field as well as to multiplicative and additive noise. Stochastic resonance is absent for Gaussian white noise. However, when the multiplicative noise has the form of an asymmetric dichotomous noise, the signal-to-noise ratio (SNR) becomes a nonmonotonic function of the correlation time and the asymmetry of noise. Moreover, the SNR turns out to be a nonmonotonic function of the frequency of the external field as well as strongly depending on the strength of the cross correlation between multiplicative and additive noise.

• Received 29 January 1999

DOI:https://doi.org/10.1103/PhysRevE.60.1494