Abstract
This note is concerned with the large deviations asymptotics estimate of the mean escape time for Lagrangian systems subjected to fast Gaussian noise. The solution to the Hamilton-Jacobi equation of the associated variational problem is derived as a sum of two terms dependent on kinetic and potential energy of the system, respectively. A closed-form solution for classes of linear and nonlinear systems is obtained. An application to a controlled pointing problem is discussed as an example.
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