Integration with respect to Lévy colored noise, with applications to SPDEs

Abstract

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.