Integration with respect to Lévy colored noise, with applications to SPDEs
In this article, we introduce a Lévy analogue of the spatially homogeneous Gaussian noise of [5], and we construct a stochastic integral with respect to this noise. The spatial covariance of the noise is given by a tempered measure μ on , whose density is given by
for a symmetric complex-valued function h. Without assuming that the Fourier transform of μ is a non-negative function, we identify a large class of integrands with respect to this noise. As an application, we examine the linear stochastic heat and wave equations driven by this type
of noise.
Keywords: Lévy processes; Primary 60G51; secondary 60H15; stochastic heat equation; stochastic integral; stochastic wave equation
Document Type: Research Article
Affiliations: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, CanadaK1N 6N5
Publication date: 04 May 2015
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