{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HZ7IV42Q7Z7AQZNFU534JLHUWS","short_pith_number":"pith:HZ7IV42Q","schema_version":"1.0","canonical_sha256":"3e7e8af350fe7e0865a5a777c4acf4b4ba3c9709367768218003aceee5a1597c","source":{"kind":"arxiv","id":"1310.4005","version":1},"attestation_state":"computed","paper":{"title":"On some applications of a symbolic representation of non-centered L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Di Nardo, I. Oliva","submitted_at":"2013-10-15T11:04:41Z","abstract_excerpt":"By using a symbolic technique known in the literature as the classical umbral calculus, we characterize two classes of polynomials related to L\\'evy processes: the Kailath-Segall and the time-space harmonic polynomials. We provide the Kailath-Segall formula in terms of cumulants and we recover simple closed-forms for several families of polynomials with respect to not centered L\\'evy processes, such as the Hermite polynomials with the Brownian motion, the Poisson-Charlier polynomials with the Poisson processes, the actuarial polynomials with the Gamma processes, the first kind Meixner polynomi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.4005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-15T11:04:41Z","cross_cats_sorted":[],"title_canon_sha256":"e334d0dde5a40671725a46af4ef03a03cda2b5db226dc1d08e837e0a957a4616","abstract_canon_sha256":"7b3c01cd124719a81bded72da7843d2e572bdcd821323aa86a7b5c16a50e468e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:25.438185Z","signature_b64":"WJ1oJYYRso2JrhhTqP6AoxkWAK0K67uzavuFRhXJAUZs/IYZOINHIgcbbtFk716cFs+xZ4E6TeIucYtUm8LcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e7e8af350fe7e0865a5a777c4acf4b4ba3c9709367768218003aceee5a1597c","last_reissued_at":"2026-05-18T03:10:25.437449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:25.437449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some applications of a symbolic representation of non-centered L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Di Nardo, I. Oliva","submitted_at":"2013-10-15T11:04:41Z","abstract_excerpt":"By using a symbolic technique known in the literature as the classical umbral calculus, we characterize two classes of polynomials related to L\\'evy processes: the Kailath-Segall and the time-space harmonic polynomials. We provide the Kailath-Segall formula in terms of cumulants and we recover simple closed-forms for several families of polynomials with respect to not centered L\\'evy processes, such as the Hermite polynomials with the Brownian motion, the Poisson-Charlier polynomials with the Poisson processes, the actuarial polynomials with the Gamma processes, the first kind Meixner polynomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4005","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.4005","created_at":"2026-05-18T03:10:25.437556+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4005v1","created_at":"2026-05-18T03:10:25.437556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4005","created_at":"2026-05-18T03:10:25.437556+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZ7IV42Q7Z7A","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZ7IV42Q7Z7AQZNF","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZ7IV42Q","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS","json":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS.json","graph_json":"https://pith.science/api/pith-number/HZ7IV42Q7Z7AQZNFU534JLHUWS/graph.json","events_json":"https://pith.science/api/pith-number/HZ7IV42Q7Z7AQZNFU534JLHUWS/events.json","paper":"https://pith.science/paper/HZ7IV42Q"},"agent_actions":{"view_html":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS","download_json":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS.json","view_paper":"https://pith.science/paper/HZ7IV42Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4005&json=true","fetch_graph":"https://pith.science/api/pith-number/HZ7IV42Q7Z7AQZNFU534JLHUWS/graph.json","fetch_events":"https://pith.science/api/pith-number/HZ7IV42Q7Z7AQZNFU534JLHUWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS/action/storage_attestation","attest_author":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS/action/author_attestation","sign_citation":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS/action/citation_signature","submit_replication":"https://pith.science/pith/HZ7IV42Q7Z7AQZNFU534JLHUWS/action/replication_record"}},"created_at":"2026-05-18T03:10:25.437556+00:00","updated_at":"2026-05-18T03:10:25.437556+00:00"}