{"paper":{"title":"Orthogonal decompositions for L\\'evy processes with an application to the gamma, Pacsal, and Meixner processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Lytvynov","submitted_at":"2002-04-08T16:50:14Z","abstract_excerpt":"It is well known that between all processes with independent increments, essentially only the Brownian motion and the Poisson process possess the chaotic representation property (CRP). Thus, a natural question appears: What is an appropriate analog of the CRP in the case of a general L\\'evy process. At least three approaches are possible here. The first one, due to\n It\\^o, uses the CRP of the Brownian motion and the Poisson process, as well as the representation of a L\\'evy process through those processes. The second approach, due to Nualart and Schoutens, consists in representing any square-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0204087","kind":"arxiv","version":5},"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"}