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arXiv · 1307.8426

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

Raluca Balan
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Abstract

In this article, we introduce a Lévy analogue of the spatially homogeneous Gaussian noise of Dalang (1999), 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 $\bR^d$, whose density is given by $|h|^2$ for a 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.

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Raluca Balan. 2013-07-31. Integration with respect to Lévy colored noise, with applications to SPDEs. https://arxiv.org/abs/1307.8426

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