{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BISXADMGDCB2MMX7LIHAT5IREX","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":"8dab7198cf398aa756d3c5ad04fabdf0bd944041338f63a73754368a9d43576f","cross_cats_sorted":["math-ph","math.MP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-01T08:54:21Z","title_canon_sha256":"16594f8c2b49388cbb46b2444e2961ec4c7a98cd868ce16f1dd43713e56c4e59"},"schema_version":"1.0","source":{"id":"1210.0312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0312","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0312v1","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0312","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"BISXADMGDCB2","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BISXADMGDCB2MMX7","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BISXADMG","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:e6310b2cca933f386f0557a158a59d80940c058ae93dbfbb4bec83b6292e53fc","target":"graph","created_at":"2026-05-18T03:44:22Z","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":"An Ornstein-Uhlenbeck (OU) process can be considered as a continuous time interpolation of the discrete time AR$(1)$ process. Departing from this fact, we analyse in this work the effect of iterating OU treated as a linear operator that maps a Wiener process onto Ornstein-Uhlenbeck process, so as to build a family of higher order Ornstein-Uhlenbeck processes, OU$(p)$, in a similar spirit as the higher order autoregressive processes AR$(p)$. We show that for $p \\ge 2$ we obtain in general a process with covariances different than those of an AR$(p)$, and that for various continuous time process","authors_text":"Alejandra Caba\\~na, Argimiro Arratia, Enrique M. Caba\\~na","cross_cats":["math-ph","math.MP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-01T08:54:21Z","title":"Modeling stationary data by a class of generalised Ornstein-Uhlenbeck processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0312","kind":"arxiv","version":1},"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:c5dee59b91b42b8abf3b775f274ce4a3e9a8eb10784b1769ecdc938fc3388620","target":"record","created_at":"2026-05-18T03:44:22Z","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":"8dab7198cf398aa756d3c5ad04fabdf0bd944041338f63a73754368a9d43576f","cross_cats_sorted":["math-ph","math.MP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-01T08:54:21Z","title_canon_sha256":"16594f8c2b49388cbb46b2444e2961ec4c7a98cd868ce16f1dd43713e56c4e59"},"schema_version":"1.0","source":{"id":"1210.0312","kind":"arxiv","version":1}},"canonical_sha256":"0a25700d861883a632ff5a0e09f51125dcbee0aafed5ee8c2bf10f1caba66f8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a25700d861883a632ff5a0e09f51125dcbee0aafed5ee8c2bf10f1caba66f8d","first_computed_at":"2026-05-18T03:44:22.785261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:22.785261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ok7p0+QkjrXi/rhVu7TDk4tQBHsv7BGL4PiScBbjftLbXMtY4jalMff4ipX/Q3HikuVDimp3LFtlfC41Z8mOAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:22.785748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5dee59b91b42b8abf3b775f274ce4a3e9a8eb10784b1769ecdc938fc3388620","sha256:e6310b2cca933f386f0557a158a59d80940c058ae93dbfbb4bec83b6292e53fc"],"state_sha256":"5301885f1277c6a64d12723a27ec2159a8c3d6edf78cf2c27eb889133ff19574"}