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-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 intensities of additive and multiplicative noises). When alpha > D, T-c, increases with increasing lambda. But when alpha < D, T-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-c-lambda curve behaves with one extremum.