We consider dynamical systems in $\mathbb{R}^d$ driven by a vector field $b(x) = - \nabla a(x)$, where $a$ is a double-well potential with some smoothness conditions. We show that these dynamical systems when subjected to a small random disturbance exhibit metastable behavior in the sense defined in [2]. More precisely, we prove that the process of moving averages along a path of such a system converges in law when properly normalized to a jump Markov process. The main tool for our analysis is the theory of Freidlin and Wentzell [7].
Publié le : 1987-10-14
Classification:
Metastability,
large deviations,
dynamical systems,
60H10,
60J05
@article{1176991977,
author = {Galves, Antonio and Olivieri, Enzo and Vares, Maria Eulalia},
title = {Metastability for a Class of Dynamical Systems Subject to Small Random Perturbations},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 1288-1305},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991977}
}
Galves, Antonio; Olivieri, Enzo; Vares, Maria Eulalia. Metastability for a Class of Dynamical Systems Subject to Small Random Perturbations. Ann. Probab., Tome 15 (1987) no. 4, pp. 1288-1305. http://gdmltest.u-ga.fr/item/1176991977/