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.

The maximum of a signal as a function of the noise intensity (“stochastic resonance”) is found in a linear system subjected to multiplicative colour noise. This result is obtained for an arbitrary dichotomous noise and for a colour noise with a short autocorrelation time. Stochastic resonance does not occur for Gaussian white noise.

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