Smoluchowski-Kramers approximation and large deviations for infinite dimensional non-gradient systems with applications to the exit problem
Probability
2014-03-25 v1
Abstract
In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that, as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular that the Smoluchowski-Kramers approximation is not only valid for small time, but, in the zero noise limit regime, can be used to approximate long-time behaviors such as exit time and exit place from a basin of attraction.
Cite
@article{arxiv.1403.5745,
title = {Smoluchowski-Kramers approximation and large deviations for infinite dimensional non-gradient systems with applications to the exit problem},
author = {Sandra Cerrai and Michael Salins},
journal= {arXiv preprint arXiv:1403.5745},
year = {2014}
}