An exactly solvable nonlinear model: Constructive effects of correlations between Gaussian noises

A system with two correlated Gaussian white noises is analysed. This system can describe both stochastic localization and long tails in the stationary distribution. Correlations between the noises can lead to a nonmonotonic behaviour of the variance as function of the intensity of one of the noises and to a stochastic resonance. A method for improving the transmission of external periodic signal by tuning parameters of the system discussed in this paper is proposed.