{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UV7EUEIFNIJQ75HEG6NT644MFI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4ec628cf31f8058bb7b55f2aefefef409872ae86979da858b19140ffbef8c510","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-03T01:41:05Z","title_canon_sha256":"646677e379872c15cbcf4dbd987e66e5ca9c548cf04a81a7792da2f6ac6422d4"},"schema_version":"1.0","source":{"id":"1507.00802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00802","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00802v2","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00802","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"UV7EUEIFNIJQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UV7EUEIFNIJQ75HE","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UV7EUEIF","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:a00e079b17a1364fcd939ac5317f92acedd8fe0d4d0527d73a4dff3b01de5c15","target":"graph","created_at":"2026-05-18T01:03:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The statistical analysis for equations driven by fractional Gaussian process (fGp) is relatively recent. The development of stochastic calculus with respect to the fGp allowed to study such models. In the present paper we consider the drift parameter estimation problem for the non-ergodic Ornstein-Uhlenbeck process defined as $dX_t=\\theta X_tdt+dG_t,\\ t\\geq0$ with an unknown parameter $\\theta>0$, where $G$ is a Gaussian process. We provide sufficient conditions, based on the properties of $G$, ensuring the strong consistency and the asymptotic distribution of our estimator $\\widetilde{\\theta}_","authors_text":"Khalifa Es-Sebaiy, Mohamed El Machkouri, Youssef Ouknine","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-03T01:41:05Z","title":"Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00802","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6f616d89422f97fedc28b9fac2148d1e4a2bbb36b47a78297dd340a031568b8f","target":"record","created_at":"2026-05-18T01:03:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4ec628cf31f8058bb7b55f2aefefef409872ae86979da858b19140ffbef8c510","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-03T01:41:05Z","title_canon_sha256":"646677e379872c15cbcf4dbd987e66e5ca9c548cf04a81a7792da2f6ac6422d4"},"schema_version":"1.0","source":{"id":"1507.00802","kind":"arxiv","version":2}},"canonical_sha256":"a57e4a11056a130ff4e4379b3f738c2a2acb5792c353191275c7c19a0899d9af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a57e4a11056a130ff4e4379b3f738c2a2acb5792c353191275c7c19a0899d9af","first_computed_at":"2026-05-18T01:03:53.034897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:53.034897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L2GYRKXdRB4eVi27T6iXlCveqqsfuGYSdzizahCSKyhgQTrVmPmp3zSP79tbCUBunT9Cmu/GPNDV1zdOTpMNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:53.035527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f616d89422f97fedc28b9fac2148d1e4a2bbb36b47a78297dd340a031568b8f","sha256:a00e079b17a1364fcd939ac5317f92acedd8fe0d4d0527d73a4dff3b01de5c15"],"state_sha256":"47a94a2b644d2aeb539b0e17404b90ce3f250d479f9b48d1a0cfe81c5b7ab6a9"}