@article{EJP500,
author = {Daniel Conus and Robert Dalang},
title = {The Non-Linear Stochastic Wave Equation in High Dimensions},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {Martingale measures; stochastic integration; stochastic wave equation; stochastic partial differential equations; moment formulae; Hölder continuity},
abstract = {We propose an extension of Walsh's classical martingale measure stochastic integral that makes it possible to integrate a general class of Schwartz distributions, which contains the fundamental solution of the wave equation, even in dimensions greater than 3. This leads to a square-integrable random-field solution to the non-linear stochastic wave equation in any dimension, in the case of a driving noise that is white in time and correlated in space. In the particular case of an affine multiplicative noise, we obtain estimates on $p$-th moments of the solution ($p\geq 1$), and we show that the solution is Hölder continuous. The Hölder exponent that we obtain is optimal.},
pages = {no. 22, 629-670},
issn = {1083-6489},
doi = {10.1214/EJP.v13-500},
url = {http://ejp.ejpecp.org/article/view/500}}