Degenerate white noise perturbations of Hamiltonian systems in
$R^2$ are studied. In particular, perturbations of a nonlinear oscillator with
1 degree of freedom are considered. If the oscillator has more than one stable
equilibrium, the long time behavior of the system is defined by a diffusion
process on a graph. Inside the edges the process is defined by a standard
averaging procedure, but to define the process for all $t > 0$ one should
add gluing conditions at the vertices. Calculation of the gluing conditions is
based on delicate Hörmander-type estimates.
Publié le : 1998-07-14
Classification:
Averaging principle,
random perturbations,
Hamiltonian systems,
60H10,
34C29,
35B20,
35H05
@article{1022855739,
author = {Freidlin, Mark and Weber, Matthias},
title = {Random perturbations of nonlinear oscillators},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 925-967},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855739}
}
Freidlin, Mark; Weber, Matthias. Random perturbations of nonlinear oscillators. Ann. Probab., Tome 26 (1998) no. 1, pp. 925-967. http://gdmltest.u-ga.fr/item/1022855739/