{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Z6JQUNYL54PRKBGLCRJEMODWVD","short_pith_number":"pith:Z6JQUNYL","schema_version":"1.0","canonical_sha256":"cf930a370bef1f1504cb1452463876a8e2662da7534fd109b19ed8fb099ad449","source":{"kind":"arxiv","id":"1306.1458","version":2},"attestation_state":"computed","paper":{"title":"Modified Euler approximation scheme for stochastic differential equations driven by fractional Brownian motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Yanghui Liu, Yaozhong Hu","submitted_at":"2013-06-06T16:24:41Z","abstract_excerpt":"For a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H> \\frac12$ it is known that the classical Euler scheme has the rate of convergence $2H-1$. In this paper we introduce a new numerical scheme which is closer to the classical Euler scheme for diffusion processes, in the sense that it has the rate of convergence $2H-\\frac12$. In particular, the rate of convergence becomes $\\frac 12$ when $H$ is formally set to $\\frac 12$ (the rate of Euler scheme for classical Brownian motion). The rate of weak convergence is also deduced for this scheme. The mai"},"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":"1306.1458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-06T16:24:41Z","cross_cats_sorted":[],"title_canon_sha256":"441043b3a5c7084da9c47e362198710c3e262b85c294ef532091c416be798553","abstract_canon_sha256":"134ff3cb113d9bd34cc671fb97e260b9aecaab554fe04414f9d9d8a5323a6271"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:35.396141Z","signature_b64":"/jXXBfdDobbbUdzRJbXxKIAclJYZ2Y3yNZ83VNwEtvS4iPcz0pcCJSKA7S1tQJ/7ORwCsvAUqoC2JOE7OjcWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf930a370bef1f1504cb1452463876a8e2662da7534fd109b19ed8fb099ad449","last_reissued_at":"2026-05-18T00:49:35.395502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:35.395502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modified Euler approximation scheme for stochastic differential equations driven by fractional Brownian motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Yanghui Liu, Yaozhong Hu","submitted_at":"2013-06-06T16:24:41Z","abstract_excerpt":"For a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H> \\frac12$ it is known that the classical Euler scheme has the rate of convergence $2H-1$. In this paper we introduce a new numerical scheme which is closer to the classical Euler scheme for diffusion processes, in the sense that it has the rate of convergence $2H-\\frac12$. In particular, the rate of convergence becomes $\\frac 12$ when $H$ is formally set to $\\frac 12$ (the rate of Euler scheme for classical Brownian motion). The rate of weak convergence is also deduced for this scheme. The mai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1458","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":"1306.1458","created_at":"2026-05-18T00:49:35.395604+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.1458v2","created_at":"2026-05-18T00:49:35.395604+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1458","created_at":"2026-05-18T00:49:35.395604+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z6JQUNYL54PR","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z6JQUNYL54PRKBGL","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z6JQUNYL","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/Z6JQUNYL54PRKBGLCRJEMODWVD","json":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD.json","graph_json":"https://pith.science/api/pith-number/Z6JQUNYL54PRKBGLCRJEMODWVD/graph.json","events_json":"https://pith.science/api/pith-number/Z6JQUNYL54PRKBGLCRJEMODWVD/events.json","paper":"https://pith.science/paper/Z6JQUNYL"},"agent_actions":{"view_html":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD","download_json":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD.json","view_paper":"https://pith.science/paper/Z6JQUNYL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.1458&json=true","fetch_graph":"https://pith.science/api/pith-number/Z6JQUNYL54PRKBGLCRJEMODWVD/graph.json","fetch_events":"https://pith.science/api/pith-number/Z6JQUNYL54PRKBGLCRJEMODWVD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD/action/storage_attestation","attest_author":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD/action/author_attestation","sign_citation":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD/action/citation_signature","submit_replication":"https://pith.science/pith/Z6JQUNYL54PRKBGLCRJEMODWVD/action/replication_record"}},"created_at":"2026-05-18T00:49:35.395604+00:00","updated_at":"2026-05-18T00:49:35.395604+00:00"}