{"paper":{"title":"Integration with respect to L\\'evy colored noise, with applications to SPDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Raluca Balan","submitted_at":"2013-07-31T18:59:50Z","abstract_excerpt":"In this article, we introduce a L\\'evy 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 $\\mu$ on $\\bR^d$, whose density is given by $|h|^2$ for a complex-valued function $h$. Without assuming that the Fourier transform of $\\mu$ 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8426","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}