{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2BBPOB3Q6SLCG7TWRNNVHQVPY4","short_pith_number":"pith:2BBPOB3Q","schema_version":"1.0","canonical_sha256":"d042f70770f496237e768b5b53c2afc70958cc3753553afbbf55e64d01d1c0d7","source":{"kind":"arxiv","id":"1412.5341","version":2},"attestation_state":"computed","paper":{"title":"Change-of-variable formula for the bi-dimensional fractional Brownian motion in Brownian time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Raghid Zeineddine","submitted_at":"2014-12-17T11:16:06Z","abstract_excerpt":"Let X^{1}, X^{2} be two independent (two-sided) fractional Brownian motions having the same Hurst parameter H in (0,1), and let Y be a standard (one-sided) Brownian motion independent of (X^{1},X^{2}). In dimension 2, fractional Brownian motion in Brownian motion time (of index H) is, by definition, the process Z_t:= (Z^1_t, Z^2_t)= (X^{1}_{Y_t},X^{2}_{Y_t}). The main result of the present paper is an Ito's type formula for f(Z_t), when f:\\R^2\\to\\R is smooth and H in [ 1/6,1). When H>1/6, the change-of-variable formula we obtain is similar to that of the classical calculus. In the critical cas"},"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":"1412.5341","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T11:16:06Z","cross_cats_sorted":[],"title_canon_sha256":"6b9becd492a2ce0d66e6d38fc468edc6b51eb6b48b87046eab18237dc5bf44b1","abstract_canon_sha256":"50bc478a8d541945e05a7eee68375bf3c519db2dad53f38e1e29bcf55e55cbee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:02.158602Z","signature_b64":"qxeEVqqdDJZtL6+mhAEfH869MlgHuoGZKpLpllkf1b61BNcKMCVJknnCxM7hJIE56H9aWZancJzXKxWKKc86Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d042f70770f496237e768b5b53c2afc70958cc3753553afbbf55e64d01d1c0d7","last_reissued_at":"2026-05-18T00:50:02.158048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:02.158048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Change-of-variable formula for the bi-dimensional fractional Brownian motion in Brownian time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Raghid Zeineddine","submitted_at":"2014-12-17T11:16:06Z","abstract_excerpt":"Let X^{1}, X^{2} be two independent (two-sided) fractional Brownian motions having the same Hurst parameter H in (0,1), and let Y be a standard (one-sided) Brownian motion independent of (X^{1},X^{2}). In dimension 2, fractional Brownian motion in Brownian motion time (of index H) is, by definition, the process Z_t:= (Z^1_t, Z^2_t)= (X^{1}_{Y_t},X^{2}_{Y_t}). The main result of the present paper is an Ito's type formula for f(Z_t), when f:\\R^2\\to\\R is smooth and H in [ 1/6,1). When H>1/6, the change-of-variable formula we obtain is similar to that of the classical calculus. In the critical cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5341","kind":"arxiv","version":2},"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":"1412.5341","created_at":"2026-05-18T00:50:02.158147+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5341v2","created_at":"2026-05-18T00:50:02.158147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5341","created_at":"2026-05-18T00:50:02.158147+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BBPOB3Q6SLC","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BBPOB3Q6SLCG7TW","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BBPOB3Q","created_at":"2026-05-18T12:28:09.283467+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/2BBPOB3Q6SLCG7TWRNNVHQVPY4","json":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4.json","graph_json":"https://pith.science/api/pith-number/2BBPOB3Q6SLCG7TWRNNVHQVPY4/graph.json","events_json":"https://pith.science/api/pith-number/2BBPOB3Q6SLCG7TWRNNVHQVPY4/events.json","paper":"https://pith.science/paper/2BBPOB3Q"},"agent_actions":{"view_html":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4","download_json":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4.json","view_paper":"https://pith.science/paper/2BBPOB3Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5341&json=true","fetch_graph":"https://pith.science/api/pith-number/2BBPOB3Q6SLCG7TWRNNVHQVPY4/graph.json","fetch_events":"https://pith.science/api/pith-number/2BBPOB3Q6SLCG7TWRNNVHQVPY4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4/action/storage_attestation","attest_author":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4/action/author_attestation","sign_citation":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4/action/citation_signature","submit_replication":"https://pith.science/pith/2BBPOB3Q6SLCG7TWRNNVHQVPY4/action/replication_record"}},"created_at":"2026-05-18T00:50:02.158147+00:00","updated_at":"2026-05-18T00:50:02.158147+00:00"}