Solution of the exit time problem for mechanical systems with fast noise

In a number of applications, an admissible domain of motion is associated with the domain of attraction of an asymptotically stable point. If noise effect is weak, escape from this domain is a rare event associated with large deviations in the system. This paper employs large deviations theory to derive the estimate of the mean time until escape from a reference domain for an mdf Lagrangian system with linear dissipation and fast additive noise. The logarithmic asymptotic of the mean exit time is found as a sum of two terms dependent on the kinetic and potential energy of the system, respectively. An exit problem in the plane is discussed as an example.