Finite-barrier corrections for multidimensional barriers in colored noise

The usual identification of reactive trajectories for the calculation of reaction rates requires very timeconsuming simulations, particularly if the environment presents memory effects. In this paper, we develop a method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.