{"paper":{"title":"SPDEs with $\\alpha$-stable L\\'evy noise: a random field approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Raluca Balan","submitted_at":"2013-03-24T18:52:04Z","abstract_excerpt":"This article is dedicated to the study of an SPDE of the form $$Lu(t,x)=\\sigma(u(t,x))\\dot{Z}(t,x) \\quad t>0, x \\in \\cO$$ with zero initial conditions and Dirichlet boundary conditions, where $\\sigma$ is a Lipschitz function, $L$ is a second-order pseudo-differential operator, $\\cO$ is a bounded domain in $\\bR^d$, and $\\dot{Z}$ is an $\\alpha$-stable L\\'evy noise with $\\alpha \\in (0,2)$, $\\alpha\\not=1$ and possibly non-symmetric tails. To give a meaning to the concept of solution, we develop a theory of stochastic integration with respect to $Z$, by generalizing the method of Gin\\'e and Marcus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5978","kind":"arxiv","version":2},"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"}