{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NYOFYJYZZ57YBPURIFY3IOVJNY","short_pith_number":"pith:NYOFYJYZ","schema_version":"1.0","canonical_sha256":"6e1c5c2719cf7f80be914171b43aa96e15006a18623d862fcb52a5e766130ca9","source":{"kind":"arxiv","id":"1708.04356","version":1},"attestation_state":"computed","paper":{"title":"On the Euler discretization error of Brownian motion about random times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A.B. Dieker, Guido Lagos","submitted_at":"2017-08-14T23:41:46Z","abstract_excerpt":"In this paper we derive weak limits for the discretization errors of sampling barrier-hitting and extreme events of Brownian motion by using the Euler discretization simulation method. Specifically, we consider the Euler discretization approximation of Brownian motion to sample barrier-hitting events, i.e. hitting for the first time a deterministic \"barrier\" function; and to sample extreme events, i.e. attaining a minimum on a given compact time interval or unbounded closed time interval. For each case we study the discretization error between the actual time the event occurs versus the time t"},"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":"1708.04356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-14T23:41:46Z","cross_cats_sorted":[],"title_canon_sha256":"b430458635a2c12021f5976f43d13b3f07067b1ba2ecd8ab573180791cefd7ee","abstract_canon_sha256":"dc73b4b188dc92c5b65cf5acd3947f38c9dbc3292b263695376430b201b684b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:59.569001Z","signature_b64":"WzXZI6wakvCCakZojFlD9CvI3DOUpL6iVpfUBGjjP391Z8gID9+pDoHuYQpp82Xm918D/Z47S0uKMTY0E5P3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e1c5c2719cf7f80be914171b43aa96e15006a18623d862fcb52a5e766130ca9","last_reissued_at":"2026-05-18T00:37:59.568517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:59.568517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Euler discretization error of Brownian motion about random times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A.B. Dieker, Guido Lagos","submitted_at":"2017-08-14T23:41:46Z","abstract_excerpt":"In this paper we derive weak limits for the discretization errors of sampling barrier-hitting and extreme events of Brownian motion by using the Euler discretization simulation method. Specifically, we consider the Euler discretization approximation of Brownian motion to sample barrier-hitting events, i.e. hitting for the first time a deterministic \"barrier\" function; and to sample extreme events, i.e. attaining a minimum on a given compact time interval or unbounded closed time interval. For each case we study the discretization error between the actual time the event occurs versus the time t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04356","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":"1708.04356","created_at":"2026-05-18T00:37:59.568608+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.04356v1","created_at":"2026-05-18T00:37:59.568608+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04356","created_at":"2026-05-18T00:37:59.568608+00:00"},{"alias_kind":"pith_short_12","alias_value":"NYOFYJYZZ57Y","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NYOFYJYZZ57YBPUR","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NYOFYJYZ","created_at":"2026-05-18T12:31:34.259226+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/NYOFYJYZZ57YBPURIFY3IOVJNY","json":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY.json","graph_json":"https://pith.science/api/pith-number/NYOFYJYZZ57YBPURIFY3IOVJNY/graph.json","events_json":"https://pith.science/api/pith-number/NYOFYJYZZ57YBPURIFY3IOVJNY/events.json","paper":"https://pith.science/paper/NYOFYJYZ"},"agent_actions":{"view_html":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY","download_json":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY.json","view_paper":"https://pith.science/paper/NYOFYJYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.04356&json=true","fetch_graph":"https://pith.science/api/pith-number/NYOFYJYZZ57YBPURIFY3IOVJNY/graph.json","fetch_events":"https://pith.science/api/pith-number/NYOFYJYZZ57YBPURIFY3IOVJNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY/action/storage_attestation","attest_author":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY/action/author_attestation","sign_citation":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY/action/citation_signature","submit_replication":"https://pith.science/pith/NYOFYJYZZ57YBPURIFY3IOVJNY/action/replication_record"}},"created_at":"2026-05-18T00:37:59.568608+00:00","updated_at":"2026-05-18T00:37:59.568608+00:00"}