{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UDGJCNB5VKKPI7U5H7FSYKY2YY","short_pith_number":"pith:UDGJCNB5","schema_version":"1.0","canonical_sha256":"a0cc91343daa94f47e9d3fcb2c2b1ac626dfda4ada7c906d4ccbad241046690a","source":{"kind":"arxiv","id":"1301.3019","version":3},"attestation_state":"computed","paper":{"title":"Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Miguel Martinez (LAMA), Pierre Etore (LJK)","submitted_at":"2013-01-14T15:43:17Z","abstract_excerpt":"In this note we propose an exact simulation algorithm for the solution of dX_t=dW_t+b(X_t)dt (1) where b is a smooth real function except at point 0 where b(0+)\\neq b(0-). The main idea is to sample an exact skeleton of X using an algorithm deduced from the convergence of the solutions of the skew perturbed equation dX^\\beta_t=dW_t+b(X^\\beta_t)dt + \\beta dL^0_t {X^\\beta} (2) towards X solution of (1) as \\beta tends to 0. In this note, we show that this convergence induces the convergence of exact simulation algorithms proposed by the authors in \\cite{etoremartinez1} for the solutions of (2) to"},"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":"1301.3019","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-14T15:43:17Z","cross_cats_sorted":[],"title_canon_sha256":"0698abec56175c665de7c5746981b82725630c16e5dda802709bbec62969ba1f","abstract_canon_sha256":"49302384b5d46b647ee36f1075838842d538f0ae66dde7d9f9b0785338ba6072"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.024530Z","signature_b64":"S2ZULgZ2UY981X8h4YMSBOjej84e2KxVg2y0spNKrtoenfIuT1e9PRx6pCuQT20OQEtLBbFNryUg1MaI9YzhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0cc91343daa94f47e9d3fcb2c2b1ac626dfda4ada7c906d4ccbad241046690a","last_reissued_at":"2026-05-18T03:11:24.023790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.023790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Miguel Martinez (LAMA), Pierre Etore (LJK)","submitted_at":"2013-01-14T15:43:17Z","abstract_excerpt":"In this note we propose an exact simulation algorithm for the solution of dX_t=dW_t+b(X_t)dt (1) where b is a smooth real function except at point 0 where b(0+)\\neq b(0-). The main idea is to sample an exact skeleton of X using an algorithm deduced from the convergence of the solutions of the skew perturbed equation dX^\\beta_t=dW_t+b(X^\\beta_t)dt + \\beta dL^0_t {X^\\beta} (2) towards X solution of (1) as \\beta tends to 0. In this note, we show that this convergence induces the convergence of exact simulation algorithms proposed by the authors in \\cite{etoremartinez1} for the solutions of (2) to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3019","kind":"arxiv","version":3},"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":"1301.3019","created_at":"2026-05-18T03:11:24.023904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.3019v3","created_at":"2026-05-18T03:11:24.023904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3019","created_at":"2026-05-18T03:11:24.023904+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDGJCNB5VKKP","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDGJCNB5VKKPI7U5","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDGJCNB5","created_at":"2026-05-18T12:28:02.375192+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/UDGJCNB5VKKPI7U5H7FSYKY2YY","json":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY.json","graph_json":"https://pith.science/api/pith-number/UDGJCNB5VKKPI7U5H7FSYKY2YY/graph.json","events_json":"https://pith.science/api/pith-number/UDGJCNB5VKKPI7U5H7FSYKY2YY/events.json","paper":"https://pith.science/paper/UDGJCNB5"},"agent_actions":{"view_html":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY","download_json":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY.json","view_paper":"https://pith.science/paper/UDGJCNB5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.3019&json=true","fetch_graph":"https://pith.science/api/pith-number/UDGJCNB5VKKPI7U5H7FSYKY2YY/graph.json","fetch_events":"https://pith.science/api/pith-number/UDGJCNB5VKKPI7U5H7FSYKY2YY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY/action/storage_attestation","attest_author":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY/action/author_attestation","sign_citation":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY/action/citation_signature","submit_replication":"https://pith.science/pith/UDGJCNB5VKKPI7U5H7FSYKY2YY/action/replication_record"}},"created_at":"2026-05-18T03:11:24.023904+00:00","updated_at":"2026-05-18T03:11:24.023904+00:00"}