{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3YQMFU2H4HRYVVGR7NZOW453XD","short_pith_number":"pith:3YQMFU2H","schema_version":"1.0","canonical_sha256":"de20c2d347e1e38ad4d1fb72eb73bbb8d82d859fe12bc30b06938bfbce20fabb","source":{"kind":"arxiv","id":"1101.0068","version":1},"attestation_state":"computed","paper":{"title":"Multivariate supOU processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ole Eiler Barndorff-Nielsen, Robert Stelzer","submitted_at":"2010-12-30T11:20:44Z","abstract_excerpt":"Univariate superpositions of Ornstein--Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure is explicitly calculated, and examples exhibit the possibility of long-range dependence. Our supOU processes are defined via homogeneous and factorizable L\\'{e}vy bases. We show that the behavior of supOU processes is particularly nice when the mean reve"},"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":"1101.0068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-30T11:20:44Z","cross_cats_sorted":[],"title_canon_sha256":"ee24c6ca1b7ff2f0c19d8fc1cdd784c26e5e3cb5be21c162d5f85a4cff69cd1c","abstract_canon_sha256":"dcd8d0f2984e9ae1f0b7481f82fb3da321e009c7e76706aea9d8ec99ee25708c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:11.099966Z","signature_b64":"zEOnhrMoQTNUYQZnngKlE0HJveTjU5CBBMEHJYEUo8vSIDKERJMVj2nT8arFUfOhbHgKbNPw1MqvGGke5BKIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de20c2d347e1e38ad4d1fb72eb73bbb8d82d859fe12bc30b06938bfbce20fabb","last_reissued_at":"2026-05-18T04:32:11.099227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:11.099227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multivariate supOU processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ole Eiler Barndorff-Nielsen, Robert Stelzer","submitted_at":"2010-12-30T11:20:44Z","abstract_excerpt":"Univariate superpositions of Ornstein--Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure is explicitly calculated, and examples exhibit the possibility of long-range dependence. Our supOU processes are defined via homogeneous and factorizable L\\'{e}vy bases. We show that the behavior of supOU processes is particularly nice when the mean reve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0068","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":"1101.0068","created_at":"2026-05-18T04:32:11.099333+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.0068v1","created_at":"2026-05-18T04:32:11.099333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0068","created_at":"2026-05-18T04:32:11.099333+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YQMFU2H4HRY","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YQMFU2H4HRYVVGR","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YQMFU2H","created_at":"2026-05-18T12:26:03.138858+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/3YQMFU2H4HRYVVGR7NZOW453XD","json":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD.json","graph_json":"https://pith.science/api/pith-number/3YQMFU2H4HRYVVGR7NZOW453XD/graph.json","events_json":"https://pith.science/api/pith-number/3YQMFU2H4HRYVVGR7NZOW453XD/events.json","paper":"https://pith.science/paper/3YQMFU2H"},"agent_actions":{"view_html":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD","download_json":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD.json","view_paper":"https://pith.science/paper/3YQMFU2H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.0068&json=true","fetch_graph":"https://pith.science/api/pith-number/3YQMFU2H4HRYVVGR7NZOW453XD/graph.json","fetch_events":"https://pith.science/api/pith-number/3YQMFU2H4HRYVVGR7NZOW453XD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD/action/storage_attestation","attest_author":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD/action/author_attestation","sign_citation":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD/action/citation_signature","submit_replication":"https://pith.science/pith/3YQMFU2H4HRYVVGR7NZOW453XD/action/replication_record"}},"created_at":"2026-05-18T04:32:11.099333+00:00","updated_at":"2026-05-18T04:32:11.099333+00:00"}