%0 Journal Article
%T Asymptotics of the solutions of the stochastic lattice wave equation
%A Tomasz Komorowski
%A Stefano Olla
%A Lenya Ryzhik
%J Physics
%D 2012
%I arXiv
%R 10.1007/s00205-013-0626-8
%X 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.
%U http://arxiv.org/abs/1203.2979v2