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In bistable systems subject to both periodic and random forcing, the signal-to-noise ratio (SNR) is maximized when the input noise is tuned near a certain value. This interesting phenomenon is termed stochastic resonance (SR) due to its characteristic signature of a sharp enhancement of the signal power spectrum corresponding to the forcing frequency. In a linear system, the input additive noise leads to a trivial decrease in the output SNR. In contrast, a dramatic increase of the SNR can be observed for a periodically modulated nonlinear potential. As a result, a majority of theoretical studies in this field were focused on non-linear systems without special concern to the nature of the noise, and it was generally believed that SR is essentially a nonlinear phenomenon. We present an analytically solvable linear model for stochastic resonance driven by multiplicative noise of the Gaussian type. A maximum of the signal-to-noise ratio is observed both as a function of the noise intensity and as a function of the autocorrelation time. The maximum appears for not too high frequencies of the applied external oscillating field immediately as soon as noise correlation is introduced, and disappears as the correlation or the frequency is increased. No resonance occurs for white noise.