{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:U5M6VERG6F726TBL77M5GXZ2RF","short_pith_number":"pith:U5M6VERG","schema_version":"1.0","canonical_sha256":"a759ea9226f17faf4c2bffd9d35f3a895f5eb8300d2f34ceda6b5aa0d7f9d9d7","source":{"kind":"arxiv","id":"1408.4502","version":1},"attestation_state":"computed","paper":{"title":"Correlation structure of time-changed fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jebessa B. Mijena","submitted_at":"2014-08-20T00:48:51Z","abstract_excerpt":"Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter $H \\in (0, 1)$ called the Hurst index. The use of time-changed processes in modeling often requires the knowledge of their second order properties such as covariance function. This paper provides the explicit expression for the correlation structure for time-changed fractional Brownian motion. Several examples useful in applications are discussed."},"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":"1408.4502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-20T00:48:51Z","cross_cats_sorted":[],"title_canon_sha256":"dc0a1bd6cceecdc76331ae5a8a2973d8e3c4489ba878099715ed85c741a2d8b2","abstract_canon_sha256":"e475befe2585b4136863ffebbf1d25a076200ec1900b1c06a1edc9528a2b6708"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:55.094280Z","signature_b64":"wsFksKZW3avxyvZF+McJ5OsK8K2/0L/UoNOLidQj0afR0b3TpDJQtKJLDANVghO+3Kb01Uc+55dw3cJgXDk/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a759ea9226f17faf4c2bffd9d35f3a895f5eb8300d2f34ceda6b5aa0d7f9d9d7","last_reissued_at":"2026-05-18T02:44:55.093751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:55.093751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlation structure of time-changed fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jebessa B. Mijena","submitted_at":"2014-08-20T00:48:51Z","abstract_excerpt":"Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter $H \\in (0, 1)$ called the Hurst index. The use of time-changed processes in modeling often requires the knowledge of their second order properties such as covariance function. This paper provides the explicit expression for the correlation structure for time-changed fractional Brownian motion. Several examples useful in applications are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4502","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":"1408.4502","created_at":"2026-05-18T02:44:55.093824+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.4502v1","created_at":"2026-05-18T02:44:55.093824+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4502","created_at":"2026-05-18T02:44:55.093824+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5M6VERG6F72","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5M6VERG6F726TBL","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5M6VERG","created_at":"2026-05-18T12:28:52.271510+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/U5M6VERG6F726TBL77M5GXZ2RF","json":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF.json","graph_json":"https://pith.science/api/pith-number/U5M6VERG6F726TBL77M5GXZ2RF/graph.json","events_json":"https://pith.science/api/pith-number/U5M6VERG6F726TBL77M5GXZ2RF/events.json","paper":"https://pith.science/paper/U5M6VERG"},"agent_actions":{"view_html":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF","download_json":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF.json","view_paper":"https://pith.science/paper/U5M6VERG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.4502&json=true","fetch_graph":"https://pith.science/api/pith-number/U5M6VERG6F726TBL77M5GXZ2RF/graph.json","fetch_events":"https://pith.science/api/pith-number/U5M6VERG6F726TBL77M5GXZ2RF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF/action/storage_attestation","attest_author":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF/action/author_attestation","sign_citation":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF/action/citation_signature","submit_replication":"https://pith.science/pith/U5M6VERG6F726TBL77M5GXZ2RF/action/replication_record"}},"created_at":"2026-05-18T02:44:55.093824+00:00","updated_at":"2026-05-18T02:44:55.093824+00:00"}