{"paper":{"title":"L\\'evy Processes and L\\'evy White Noise as Tempered Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Robert C. Dalang, Thomas Humeau","submitted_at":"2015-09-17T14:51:23Z","abstract_excerpt":"We identify a necessary and sufficient condition for a L\\'evy white noise to be a tempered distribution. More precisely, we show that if the L\\'evy measure associated with this noise has a positive absolute moment, then the L\\'evy white noise almost surely takes values in the space of tempered distributions. If the L\\'evy measure does not have a positive absolute moment of any order, then the event on which the L\\'evy white noise is a tempered distribution has probability zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05274","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"}