Asymptotics of the solutions of the stochastic lattice wave equation
Mathematical Physics
2015-06-04 v2 math.MP
Abstract
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic.
Keywords
Cite
@article{arxiv.1203.2979,
title = {Asymptotics of the solutions of the stochastic lattice wave equation},
author = {Tomasz Komorowski and Stefano Olla and Lenya Ryzhik},
journal= {arXiv preprint arXiv:1203.2979},
year = {2015}
}