Stationary solutions to a Fokker--Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an unlimited growth. Positive correlations between the noises can lead to a minimum of the variance of the process and to the stochastic resonance if the system is additionally driven by a periodic signal.

PACS numbers: 05.40.Ca, 02.50.Ey, 87.23.Cc