Dynamical properties of a bistable kinetic model with correlated noises

We consider a bistable kinetic model driven by additive and multiplicative noises which are correlated with each other. By means of the projection operator method, we study the effects of the correlation intensity between the two noises on the relaxation time, corresponding to the fluctuation of the state variable in the stationary state. It is found that the presence of correlations between the additive and multiplicative noises causes the relaxation time to decrease when the additive noise intensity is small enough, but to increase when the additive noise intensity is larger. The larger the correlation strength, the more pronounced are the effects on the relaxation time. Hence, the correlations between noises play a very important role on the decay of fluctuations in the stationary state.