We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous Gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations. For comparison, we also derive bounds on moments of the solution to the stochastic heat equation with the same linear multiplicative noise.
@article{1257529897,
author = {Dalang, Robert C. and Mueller, Carl},
title = {Intermittency properties in a hyperbolic Anderson problem},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 1150-1164},
language = {en},
url = {http://dml.mathdoc.fr/item/1257529897}
}
Dalang, Robert C.; Mueller, Carl. Intermittency properties in a hyperbolic Anderson problem. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 1150-1164. http://gdmltest.u-ga.fr/item/1257529897/