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Under finite $(p,q)$-variation regularity assumptions in the sense of two-dimensional Young integration theory, we establish a pathwise local-time decomposition\n  $$F_t(X_t) = F_0(X_0)+ \\int_0^t\\nabla^hF_s(X_s)ds + \\int_0^t\\nabla^wF_s(X_s)dX(s) - \\frac{1}{2}\\int_{-\\infty}^{+\\infty}\\int_0^t(\\nabla^w_xF_s)(^{x}X_s)d_{(s,x)}\\ell^x(s).$$ Here, $X_t= \\{X(s); 0\\le s\\le t\\}$ is the continuous semimartingale path up to time $t\\in [0,T]$, $\\nabla^h$ is the horizontal deriv"},"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":"1505.00879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-05T04:33:17Z","cross_cats_sorted":[],"title_canon_sha256":"4f2064f69c8c8f80f42df5d7bd7dec977dbdf6e8e9684de95e84429ff83faab6","abstract_canon_sha256":"c7bdc8a9045834279195d462cb2ece1dd456a4617bf0682724ff1e6072dc0340"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:26.200950Z","signature_b64":"2GKgADyyo1Ckr3v5rF+wwdT+gqx/r12AOOMLUQzHMkBE5Cb5nxD7NKKI1otZW2BtNXfrMFbMxR9A6U7P7FggCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"085bce7c7be284a1bdb030f3e84fdd12074d354f7e5e056a56ce8077adf6f63c","last_reissued_at":"2026-05-18T02:07:26.199832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:26.199832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Path-dependent It\\^o formulas under finite $(p,q)$-variation regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alberto Ohashi, Evelina Shamarova, Nikolai N. 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Under finite $(p,q)$-variation regularity assumptions in the sense of two-dimensional Young integration theory, we establish a pathwise local-time decomposition\n  $$F_t(X_t) = F_0(X_0)+ \\int_0^t\\nabla^hF_s(X_s)ds + \\int_0^t\\nabla^wF_s(X_s)dX(s) - \\frac{1}{2}\\int_{-\\infty}^{+\\infty}\\int_0^t(\\nabla^w_xF_s)(^{x}X_s)d_{(s,x)}\\ell^x(s).$$ Here, $X_t= \\{X(s); 0\\le s\\le t\\}$ is the continuous semimartingale path up to time $t\\in [0,T]$, $\\nabla^h$ is the horizontal deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00879","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":"1505.00879","created_at":"2026-05-18T02:07:26.199908+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00879v2","created_at":"2026-05-18T02:07:26.199908+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00879","created_at":"2026-05-18T02:07:26.199908+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBN447D34KCK","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBN447D34KCKDPNQ","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBN447D3","created_at":"2026-05-18T12:29:14.074870+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/BBN447D34KCKDPNQGDZ6QT65CI","json":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI.json","graph_json":"https://pith.science/api/pith-number/BBN447D34KCKDPNQGDZ6QT65CI/graph.json","events_json":"https://pith.science/api/pith-number/BBN447D34KCKDPNQGDZ6QT65CI/events.json","paper":"https://pith.science/paper/BBN447D3"},"agent_actions":{"view_html":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI","download_json":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI.json","view_paper":"https://pith.science/paper/BBN447D3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00879&json=true","fetch_graph":"https://pith.science/api/pith-number/BBN447D34KCKDPNQGDZ6QT65CI/graph.json","fetch_events":"https://pith.science/api/pith-number/BBN447D34KCKDPNQGDZ6QT65CI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI/action/storage_attestation","attest_author":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI/action/author_attestation","sign_citation":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI/action/citation_signature","submit_replication":"https://pith.science/pith/BBN447D34KCKDPNQGDZ6QT65CI/action/replication_record"}},"created_at":"2026-05-18T02:07:26.199908+00:00","updated_at":"2026-05-18T02:07:26.199908+00:00"}