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

• Robert C. Dalang ^[1] ; Olivier Lévêque ^[1]
  1. [1] Ecole Polytechnique Fédérale de Lausanne
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 1, 2, 2004, págs. 1068-1099
• Idioma: inglés
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• Resumen

  • We study a class of linear hyperbolic stochastic partial differential equations in bounded domains, which 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.