Effects of cross-correlated noises on the relaxation time of the bistable system

The stationary correlation function and the associated relaxation time for a general system driven by cross-correlated white noises are derived, by virtue of a Stratonovich-like ansatz. The effects of correlated noises on the relaxation time of a bistable kinetic model coupled to an additive and a multiplicative white noises are studied. It is proved that for small fluctuations the relaxation time T_\rm c as a function of \lambda (the correlated intensity between noises) exhibits very different behaviours for \alpha < D and for \alpha > D (\alpha and D, respectively, stand for the ntensities of additive and multiplicative noises). When \alpha < D, T_\rm c increases with increasing \lambda. But when \alpha < D, T_\rm c increases with \lambda for the case of weak correlated noises and sharply decreases with \lambda for the case of strong correlated noises, and thus T_\rm c-\lambda curve behaves with one extremum.