Second-order linear hyperbolic SPDEs driven by isotropic Gaussian noise on a sphere

• Published in: Annals of Applied Probability, vol. 32, num. 1B, p. 1068-1099
• Publication date: 2004

We study a class of linear hyperbolic stochastic partial differential equations in bounded domains, that includes the wave equation and the telegraph equation, driven by Gaussian noise that is white in time but not in space. We give necessary and sufficient conditions on the spatial correlation of the noise for the existence (and uniqueness) of square-integrable solutions. In the particular case where the domain is a ball and the noise is concentrated on a sphere, we characterize the isotropic Gaussian noises with this property. We also give explicit necessary and sufficient conditions when the domain is a hypercube and the Gaussian noise is concentrated on a hyperplane.

Keywords: stochastic partial differential equations ; isotropic ; Gaussian noise ; hyperbolic equations

Reference

• PROB-ARTICLE-2004-004
• doi:NA
• View record in Web of Science

Record created on 2008-12-01, modified on 2012-03-21