1203.2979 (Tomasz Komorowski et al.)

Asymptotics of the solutions of the stochastic lattice wave equation    [PDF]

Tomasz Komorowski, Stefano Olla, Lenya Ryzhik

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.

View original: http://arxiv.org/abs/1203.2979