{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EJDJOJLUVZJ23SVBA5F2C3AUZL","short_pith_number":"pith:EJDJOJLU","schema_version":"1.0","canonical_sha256":"2246972574ae53adcaa1074ba16c14caf66f8a7100072f36e0edd0457947b535","source":{"kind":"arxiv","id":"1001.3344","version":1},"attestation_state":"computed","paper":{"title":"A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas Neuenkirch, Aur\\'elien Deya (IECN), Samy Tindel (IECN)","submitted_at":"2010-01-19T16:12:16Z","abstract_excerpt":"In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second order Taylor expansion, where the usual Levy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds for the discretisation of the Levy area terms."},"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":"1001.3344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-19T16:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"0ecdfa073f17c0b067581de8fc300459c7b2fd7f7e017eb305f54d527bc2106e","abstract_canon_sha256":"ccaefdc7b4bb6daee8c2eba1398afde0c503c0e95819ac773c089e01ba4f6b23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:42.324931Z","signature_b64":"WaU/h4En/leK4xya9miJniTHjrRw4CJ51B1+dKidfdVOuxPAMzUuKAmg55sLlHV93828duY/gLMwVTq63XCPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2246972574ae53adcaa1074ba16c14caf66f8a7100072f36e0edd0457947b535","last_reissued_at":"2026-05-18T02:09:42.324123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:42.324123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas Neuenkirch, Aur\\'elien Deya (IECN), Samy Tindel (IECN)","submitted_at":"2010-01-19T16:12:16Z","abstract_excerpt":"In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second order Taylor expansion, where the usual Levy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds for the discretisation of the Levy area terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3344","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":"1001.3344","created_at":"2026-05-18T02:09:42.324251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.3344v1","created_at":"2026-05-18T02:09:42.324251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3344","created_at":"2026-05-18T02:09:42.324251+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJDJOJLUVZJ2","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJDJOJLUVZJ23SVB","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJDJOJLU","created_at":"2026-05-18T12:26:06.534383+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/EJDJOJLUVZJ23SVBA5F2C3AUZL","json":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL.json","graph_json":"https://pith.science/api/pith-number/EJDJOJLUVZJ23SVBA5F2C3AUZL/graph.json","events_json":"https://pith.science/api/pith-number/EJDJOJLUVZJ23SVBA5F2C3AUZL/events.json","paper":"https://pith.science/paper/EJDJOJLU"},"agent_actions":{"view_html":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL","download_json":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL.json","view_paper":"https://pith.science/paper/EJDJOJLU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.3344&json=true","fetch_graph":"https://pith.science/api/pith-number/EJDJOJLUVZJ23SVBA5F2C3AUZL/graph.json","fetch_events":"https://pith.science/api/pith-number/EJDJOJLUVZJ23SVBA5F2C3AUZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL/action/storage_attestation","attest_author":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL/action/author_attestation","sign_citation":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL/action/citation_signature","submit_replication":"https://pith.science/pith/EJDJOJLUVZJ23SVBA5F2C3AUZL/action/replication_record"}},"created_at":"2026-05-18T02:09:42.324251+00:00","updated_at":"2026-05-18T02:09:42.324251+00:00"}