Three variable models in multivariate transient stochastic dynamics. The presence of constant external force

In this work we show that the generalized formalism of the Quasideterministic (QD) approach and its connection with the Nonlinear Relaxation Times (NLRT), is absolutely consistent with 3×3 matricial models whose elements of matrix are all different from zero, in the context of both Gaussian white and colored noise. In the absence of external force, more general results than those reported in Refs. [1,2] are given. The consistency of the formalism with such models in the presence of constant external force is also verified for Gaussian white noise.