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January 2004 Second-order linear hyperbolic SPDEs driven by isotropic Gaussian noise on a sphere
Robert C. Dalang, Olivier Lévêque
Ann. Probab. 32(1B): 1068-1099 (January 2004). DOI: 10.1214/aop/1079021472


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.


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Robert C. Dalang. Olivier Lévêque. "Second-order linear hyperbolic SPDEs driven by isotropic Gaussian noise on a sphere." Ann. Probab. 32 (1B) 1068 - 1099, January 2004.


Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1046.60058
MathSciNet: MR2044674
Digital Object Identifier: 10.1214/aop/1079021472

Primary: 60H15
Secondary: 35R60 , 60G15

Keywords: Hyperbolic equations , isotropic Gaussian noise , Stochastic partial differential equations

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 1B • January 2004
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