Approximation and support theorem for a wave equation in two space dimensions

Citation
A. Millet et M. Sanz-sole, Approximation and support theorem for a wave equation in two space dimensions, BERNOULLI, 6(5), 2000, pp. 887-915
Citations number
6
Categorie Soggetti
Mathematics
Journal title
BERNOULLI
ISSN journal
13507265 → ACNP
Volume
6
Issue
5
Year of publication
2000
Pages
887 - 915
Database
ISI
SICI code
1350-7265(200010)6:5<887:AASTFA>2.0.ZU;2-C
Abstract
We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coe fficients, approximation in the L-p-norm for p greater than or equal to 1 i s also proved.