The transition rate of a double well system driven by cross-correlated noises

The transition rate of a double well system driven by cross-correlated noises has been investigated, in when the correlation times between the noises are nonzero. From numerical computation, we find followings: (1) The transition rate decreases as the λ (λ is the strength of the correlations between noises) increases. (2) The transition rate increases as the τ (τ is the correlation time between noises) increases. It imglies that τ and λ play opposite roles in the transition rate of the system (3). For the case of perfectly correlated noises (λ = 1), there is no the suppressed phenomenon in the double well system with cross-correlated noise sources.