{"paper":{"title":"L\\'{e}vy driven linear and semilinear stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Berger","submitted_at":"2019-07-03T13:14:58Z","abstract_excerpt":"The goal of this paper is twofold. In the first part we will study L\\'{e}vy white noise in different distributional spaces and solve equations of the type $p(D)s=q(D)\\dot{L}$, where $p$ and $q$ are polynomials. Furthermore, we will study measurability of $s$ in Besov spaces. By using this result we will prove that stochastic partial differential equations of the form \\begin{align*} p(D)u=g(\\cdot,u)+\\dot{L} \\end{align*} have measurable solutions in weighted Besov spaces, where $p(D)$ is a partial differential operator in a certain class, $g:\\mathbb{R}^d\\times \\mathbb{C}\\to \\mathbb{R}$ satisfies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01926","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"}