Smoluchowski-Kramers approximation and large deviations for infinite dimensional gradient systems
Probability
2014-03-25 v1
Abstract
In this paper, we explicitly calculate the quasi-potentials for the damped semilinear stochastic wave equation when the system is of gradient type. We show that in this case the infimum of the quasi-potential with respect to all possible velocities does not depend on the density of the mass and does coincide with 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 can be used to approximate long time behavior in the zero noise limit, such as exit time and exit place from a basin of attraction.
Cite
@article{arxiv.1403.5743,
title = {Smoluchowski-Kramers approximation and large deviations for infinite dimensional gradient systems},
author = {Sandra Cerrai and Michael Salins},
journal= {arXiv preprint arXiv:1403.5743},
year = {2014}
}