Stochastic escape processes from a non-symmetric potential normal form .2. The marginal case

The first-passage time distribution to reach the attractor of the stochastic differential equation (X) over dot(t) = a(X(2) - X(3)) + root epsilon xi(t) is analytically obtained by using a previously reported scheme: the stochastic path perturbation approach. A second-order perturbation theory, in the small noise parameter root epsilon, is introduced to analyse the random escape, of the stochastic paths, from the marginal unstable state X = 0. The anomalous fluctuation of the phase-space variable X(t) is analytically calculated by using the instanton-like approximation. We have carried out Monte Carlo simulations showing good agreement with our theoretical predictions.