{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CADPNKXIZVDFUOLCQTAV6DBIR6","short_pith_number":"pith:CADPNKXI","schema_version":"1.0","canonical_sha256":"1006f6aae8cd465a396284c15f0c288f88d34099185a0bed9168234b67683191","source":{"kind":"arxiv","id":"1801.00120","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic expansion of Skorohod integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, nakahiro yoshida","submitted_at":"2017-12-30T11:51:24Z","abstract_excerpt":"Asymptotic expansion of the distribution of a perturbation $Z_n$ of a Skorohod integral jointly with a reference variable $X_n$ is derived. We introduce a second-order interpolation formula in frequency domain to expand a characteristic functional and combine it with the scheme developed in the martingale expansion. The second-order interpolation and Fourier inversion give asymptotic expansion of the expectation $E[f(Z_n,X_n)]$ for differentiable functions $f$ and also measurable functions $f$. In the latter case, the interpolation method connects the two non-degeneracies of variables for fini"},"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":"1801.00120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-30T11:51:24Z","cross_cats_sorted":[],"title_canon_sha256":"8561347e1626e6e7326587d5f9ce21e9eb347bf633a438b0dfe7549b00194a4f","abstract_canon_sha256":"fb4513f7de436850ab15f6794901c8bc999bcadd06bcfa46fd8875927eb579de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:59.351133Z","signature_b64":"fRustWlWKEjxe/uIb3D4cGKlZSZnZabiBxbfjNiBNVeja7tJP0j26VinZVexBFdiYHqNwPyMtD+lSBJu931/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1006f6aae8cd465a396284c15f0c288f88d34099185a0bed9168234b67683191","last_reissued_at":"2026-05-18T00:26:59.350462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:59.350462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic expansion of Skorohod integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, nakahiro yoshida","submitted_at":"2017-12-30T11:51:24Z","abstract_excerpt":"Asymptotic expansion of the distribution of a perturbation $Z_n$ of a Skorohod integral jointly with a reference variable $X_n$ is derived. We introduce a second-order interpolation formula in frequency domain to expand a characteristic functional and combine it with the scheme developed in the martingale expansion. The second-order interpolation and Fourier inversion give asymptotic expansion of the expectation $E[f(Z_n,X_n)]$ for differentiable functions $f$ and also measurable functions $f$. In the latter case, the interpolation method connects the two non-degeneracies of variables for fini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00120","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":"1801.00120","created_at":"2026-05-18T00:26:59.350562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.00120v1","created_at":"2026-05-18T00:26:59.350562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00120","created_at":"2026-05-18T00:26:59.350562+00:00"},{"alias_kind":"pith_short_12","alias_value":"CADPNKXIZVDF","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CADPNKXIZVDFUOLC","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CADPNKXI","created_at":"2026-05-18T12:31:10.602751+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/CADPNKXIZVDFUOLCQTAV6DBIR6","json":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6.json","graph_json":"https://pith.science/api/pith-number/CADPNKXIZVDFUOLCQTAV6DBIR6/graph.json","events_json":"https://pith.science/api/pith-number/CADPNKXIZVDFUOLCQTAV6DBIR6/events.json","paper":"https://pith.science/paper/CADPNKXI"},"agent_actions":{"view_html":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6","download_json":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6.json","view_paper":"https://pith.science/paper/CADPNKXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.00120&json=true","fetch_graph":"https://pith.science/api/pith-number/CADPNKXIZVDFUOLCQTAV6DBIR6/graph.json","fetch_events":"https://pith.science/api/pith-number/CADPNKXIZVDFUOLCQTAV6DBIR6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6/action/storage_attestation","attest_author":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6/action/author_attestation","sign_citation":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6/action/citation_signature","submit_replication":"https://pith.science/pith/CADPNKXIZVDFUOLCQTAV6DBIR6/action/replication_record"}},"created_at":"2026-05-18T00:26:59.350562+00:00","updated_at":"2026-05-18T00:26:59.350562+00:00"}