Stochastic perturbations of generalized Landau expansion

The stochastic version of the Landau equation is obtained from the Lorentz model for small value of the bifurcating parameter using the central manifold theory. It is shown that the variance of the noise perturbing the amplitude equation depends on the nonlinear coupling between the degrees of freedom in a nontrivial way. The method used to derive the Landau equation can also be applied to compute the average exit time for nonpotential stochastic differential equations