{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UUM4NEYLYEKQHMVJHND7UY46QP","short_pith_number":"pith:UUM4NEYL","schema_version":"1.0","canonical_sha256":"a519c6930bc11503b2a93b47fa639e83dfc6518388b4ab1af2986d9168c76ecf","source":{"kind":"arxiv","id":"1304.7531","version":3},"attestation_state":"computed","paper":{"title":"Nonlinear Hawkes Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lingjiong Zhu","submitted_at":"2013-04-28T22:34:23Z","abstract_excerpt":"The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past events. There are applications in finance, neuroscience, genome analysis, seismology, sociology, criminology and many other fields. We first survey the known results about the theory and applications of both linear and nonlinear Hawkes processes. Then, we obtain the central limit theorem and process-level, i.e. level-3 large deviations for nonlinear Hawkes proce"},"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":"1304.7531","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T22:34:23Z","cross_cats_sorted":[],"title_canon_sha256":"274bc2fd259fbf0eb3a79e7d79d4d6fb52b6b2bed242c3d5f9c3ac34f99a7e04","abstract_canon_sha256":"40ef6c4725e0fe274dfe0764a896902d97ae5894a419e3a04f175bab14804e6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:08.990114Z","signature_b64":"CvbolApAm+HIJadNOoYb6LNcwL8OXAaB5XZpSEF4nEcm4E018d/gfjiAg+CMFVPxZeVHkaJbALAwdlVcYxUpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a519c6930bc11503b2a93b47fa639e83dfc6518388b4ab1af2986d9168c76ecf","last_reissued_at":"2026-05-18T03:20:08.989595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:08.989595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Hawkes Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lingjiong Zhu","submitted_at":"2013-04-28T22:34:23Z","abstract_excerpt":"The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past events. There are applications in finance, neuroscience, genome analysis, seismology, sociology, criminology and many other fields. We first survey the known results about the theory and applications of both linear and nonlinear Hawkes processes. Then, we obtain the central limit theorem and process-level, i.e. level-3 large deviations for nonlinear Hawkes proce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7531","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":""},"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":"1304.7531","created_at":"2026-05-18T03:20:08.989676+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7531v3","created_at":"2026-05-18T03:20:08.989676+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7531","created_at":"2026-05-18T03:20:08.989676+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUM4NEYLYEKQ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUM4NEYLYEKQHMVJ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUM4NEYL","created_at":"2026-05-18T12:28:02.375192+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/UUM4NEYLYEKQHMVJHND7UY46QP","json":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP.json","graph_json":"https://pith.science/api/pith-number/UUM4NEYLYEKQHMVJHND7UY46QP/graph.json","events_json":"https://pith.science/api/pith-number/UUM4NEYLYEKQHMVJHND7UY46QP/events.json","paper":"https://pith.science/paper/UUM4NEYL"},"agent_actions":{"view_html":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP","download_json":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP.json","view_paper":"https://pith.science/paper/UUM4NEYL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7531&json=true","fetch_graph":"https://pith.science/api/pith-number/UUM4NEYLYEKQHMVJHND7UY46QP/graph.json","fetch_events":"https://pith.science/api/pith-number/UUM4NEYLYEKQHMVJHND7UY46QP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP/action/storage_attestation","attest_author":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP/action/author_attestation","sign_citation":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP/action/citation_signature","submit_replication":"https://pith.science/pith/UUM4NEYLYEKQHMVJHND7UY46QP/action/replication_record"}},"created_at":"2026-05-18T03:20:08.989676+00:00","updated_at":"2026-05-18T03:20:08.989676+00:00"}