{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PVYDWR6VBHVSNLHNBQ7ACOFHEQ","short_pith_number":"pith:PVYDWR6V","schema_version":"1.0","canonical_sha256":"7d703b47d509eb26aced0c3e0138a7242dbc4199e95b15ec2b5296377cd838aa","source":{"kind":"arxiv","id":"1606.03854","version":1},"attestation_state":"computed","paper":{"title":"The Order Barrier for Strong Approximation of Rough Volatility Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.PR","authors_text":"Andreas Neuenkirch, Taras Shalaiko","submitted_at":"2016-06-13T08:26:40Z","abstract_excerpt":"We study the strong approximation of a rough volatility model, in which the log-volatility is given by a fractional Ornstein-Uhlenbeck process with Hurst parameter $H<1/2$. Our methods are based on an equidistant discretization of the volatility process and of the driving Brownian motions, respectively. For the root mean-square error at a single point the optimal rate of convergence that can be achieved by such methods is $n^{-H}$, where $n$ denotes the number of subintervals of the discretization. This rate is in particular obtained by the Euler method and an Euler-trapezoidal type scheme."},"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":"1606.03854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-13T08:26:40Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"52c2d314429f1e5c5b2f81d0272f8e66f49b6fff90095ff654a6e56ed90e82d7","abstract_canon_sha256":"a4c9ea05b459ec16230ef820471e784fb62df8cd9b4fd2b4311d2c97a8ce6ecd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:32.894976Z","signature_b64":"X82GC44aPVNO9gOynqElrd1Uygm0f2ApLNHzM4Lifv2zdMZpCjnWEseRJfhSLULIM+W6jrCanUmQXaJ7M/Y2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d703b47d509eb26aced0c3e0138a7242dbc4199e95b15ec2b5296377cd838aa","last_reissued_at":"2026-05-18T01:12:32.894530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:32.894530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Order Barrier for Strong Approximation of Rough Volatility Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.PR","authors_text":"Andreas Neuenkirch, Taras Shalaiko","submitted_at":"2016-06-13T08:26:40Z","abstract_excerpt":"We study the strong approximation of a rough volatility model, in which the log-volatility is given by a fractional Ornstein-Uhlenbeck process with Hurst parameter $H<1/2$. Our methods are based on an equidistant discretization of the volatility process and of the driving Brownian motions, respectively. For the root mean-square error at a single point the optimal rate of convergence that can be achieved by such methods is $n^{-H}$, where $n$ denotes the number of subintervals of the discretization. This rate is in particular obtained by the Euler method and an Euler-trapezoidal type scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03854","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":"1606.03854","created_at":"2026-05-18T01:12:32.894605+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.03854v1","created_at":"2026-05-18T01:12:32.894605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03854","created_at":"2026-05-18T01:12:32.894605+00:00"},{"alias_kind":"pith_short_12","alias_value":"PVYDWR6VBHVS","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PVYDWR6VBHVSNLHN","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PVYDWR6V","created_at":"2026-05-18T12:30:39.010887+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/PVYDWR6VBHVSNLHNBQ7ACOFHEQ","json":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ.json","graph_json":"https://pith.science/api/pith-number/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/graph.json","events_json":"https://pith.science/api/pith-number/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/events.json","paper":"https://pith.science/paper/PVYDWR6V"},"agent_actions":{"view_html":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ","download_json":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ.json","view_paper":"https://pith.science/paper/PVYDWR6V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.03854&json=true","fetch_graph":"https://pith.science/api/pith-number/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/action/storage_attestation","attest_author":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/action/author_attestation","sign_citation":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/action/citation_signature","submit_replication":"https://pith.science/pith/PVYDWR6VBHVSNLHNBQ7ACOFHEQ/action/replication_record"}},"created_at":"2026-05-18T01:12:32.894605+00:00","updated_at":"2026-05-18T01:12:32.894605+00:00"}