Estimation of the Mean Escape Time in Lagrangian Systems with Weak Noise
Abstract
In a number of applications, an admissible domain of the perturbed motion is associated with the domain of attraction of a stable equilibrium of the unperturbed system. If noise is weak, escape from the reference domain is a rare event associated with large deviations in the system. Despite the well developed large deviations theory, estimation of the statistical parameters for the multidimensional nonlinear systems remains difficult. This paper develops an asymptotic approximation of the mean escape time for a weakly perturbed Lagrangian system. The estimate is found explicitly, as a function of the kinetic and potential energy and the dissipation function of the system.
