Smoluchowski-Kramers approximation and large deviations for infinite-dimensional nongradient systems with applications to the exit problem
Files
Accepted manuscript
Date
2016-07-01
Authors
Cerrai, Sandra
Salins, Michael
Version
Accepted manuscript
OA Version
Citation
Sandra Cerrai, Michael Salins. 2016. "SMOLUCHOWSKI-KRAMERS APPROXIMATION AND LARGE DEVIATIONS FOR INFINITE-DIMENSIONAL NONGRADIENT SYSTEMS WITH APPLICATIONS TO THE EXIT PROBLEM." ANNALS OF PROBABILITY, Volume 44, Issue 4, pp. 2591 - 2642 (52). https://doi.org/10.1214/15-AOP1029
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.