{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TMZSY3DSNSPBCDSYM223Y2QX6N","short_pith_number":"pith:TMZSY3DS","schema_version":"1.0","canonical_sha256":"9b332c6c726c9e110e5866b5bc6a17f345ca9c620baa795d1b5f0cc67e87958f","source":{"kind":"arxiv","id":"1109.0933","version":1},"attestation_state":"computed","paper":{"title":"Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ciprian Tudor (LPP), Jorge Clarke De La Cerda","submitted_at":"2011-09-05T15:18:13Z","abstract_excerpt":"We will study the least square estimator $\\hat{\\theta}_{T,S}$ for the drift parameter $\\theta$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation \nX_{t,s}= -\\theta \\int^{t}_{0} \\int^{s}_{0} X_{v,u}dvdu + B^{\\alpha, \\beta}_{t,s}, \\qquad (t,s) \\in [0,T]\\times [0,S]\ndriven by the fractional Brownian sheet $B^{\\alpha ,\\beta}$ with Hurst parameters $\\alpha, \\beta$ in $(1/2, 5/8)$. Using the properties of multiple Wiener-It\\^o integrals we prove that the estimator is strongly consistent for the parameter $\\theta$. In contrast to the one-dimensional c"},"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":"1109.0933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-05T15:18:13Z","cross_cats_sorted":[],"title_canon_sha256":"d82fe4f6f2ab03f82b10140c2fa16777627be9839bdae6edae0606ca928a685d","abstract_canon_sha256":"fea6de7b6833c74f5b315fa0daded166d0735d9d307217c8c4edac0e33b203c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:06.358388Z","signature_b64":"hGnn9DGheG0eZsf4MqZjKwX/N6I1HvBQh8x5Vc7kiNCBLfhWe7FI9jqgx26SK+PziTNHttr/3y2DjU7ddSNnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b332c6c726c9e110e5866b5bc6a17f345ca9c620baa795d1b5f0cc67e87958f","last_reissued_at":"2026-05-18T04:14:06.357845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:06.357845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ciprian Tudor (LPP), Jorge Clarke De La Cerda","submitted_at":"2011-09-05T15:18:13Z","abstract_excerpt":"We will study the least square estimator $\\hat{\\theta}_{T,S}$ for the drift parameter $\\theta$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation \nX_{t,s}= -\\theta \\int^{t}_{0} \\int^{s}_{0} X_{v,u}dvdu + B^{\\alpha, \\beta}_{t,s}, \\qquad (t,s) \\in [0,T]\\times [0,S]\ndriven by the fractional Brownian sheet $B^{\\alpha ,\\beta}$ with Hurst parameters $\\alpha, \\beta$ in $(1/2, 5/8)$. Using the properties of multiple Wiener-It\\^o integrals we prove that the estimator is strongly consistent for the parameter $\\theta$. In contrast to the one-dimensional c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0933","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":"1109.0933","created_at":"2026-05-18T04:14:06.357926+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.0933v1","created_at":"2026-05-18T04:14:06.357926+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0933","created_at":"2026-05-18T04:14:06.357926+00:00"},{"alias_kind":"pith_short_12","alias_value":"TMZSY3DSNSPB","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TMZSY3DSNSPBCDSY","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TMZSY3DS","created_at":"2026-05-18T12:26:42.757692+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/TMZSY3DSNSPBCDSYM223Y2QX6N","json":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N.json","graph_json":"https://pith.science/api/pith-number/TMZSY3DSNSPBCDSYM223Y2QX6N/graph.json","events_json":"https://pith.science/api/pith-number/TMZSY3DSNSPBCDSYM223Y2QX6N/events.json","paper":"https://pith.science/paper/TMZSY3DS"},"agent_actions":{"view_html":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N","download_json":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N.json","view_paper":"https://pith.science/paper/TMZSY3DS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.0933&json=true","fetch_graph":"https://pith.science/api/pith-number/TMZSY3DSNSPBCDSYM223Y2QX6N/graph.json","fetch_events":"https://pith.science/api/pith-number/TMZSY3DSNSPBCDSYM223Y2QX6N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N/action/storage_attestation","attest_author":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N/action/author_attestation","sign_citation":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N/action/citation_signature","submit_replication":"https://pith.science/pith/TMZSY3DSNSPBCDSYM223Y2QX6N/action/replication_record"}},"created_at":"2026-05-18T04:14:06.357926+00:00","updated_at":"2026-05-18T04:14:06.357926+00:00"}