{"paper":{"title":"Integrability and Approximability of Solutions to the Stationary Diffusion Equation with L\\'evy Coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.AP","authors_text":"Hanno Gottschalk, Marco Reese, Oliver G. Ernst, Thomas Kalmes, Toni Kowalewitz","submitted_at":"2020-10-28T12:14:34Z","abstract_excerpt":"We investigate the stationary diffusion equation with a coefficient given by a (transformed) L\\'evy random field. L\\'evy random fields are constructed by smoothing L\\'evy noise fields with kernels from the Mat\\'ern class. We show that L\\'evy noise naturally extends Gaussian white noise within Minlos' theory of generalized random fields. Results on the distributional path spaces of L\\'evy noise are derived as well as the amount of smoothing to ensure such distributions become continuous paths. Given this, we derive results on the pathwise existence and measurability of solutions to the random b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.14912","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.14912/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}