{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7PJPG273DGVCGHER75OA36AMLR","short_pith_number":"pith:7PJPG273","schema_version":"1.0","canonical_sha256":"fbd2f36bfb19aa231c91ff5c0df80c5c7c0b79f07916d5cf8a3a27da1a3751ad","source":{"kind":"arxiv","id":"1303.3717","version":1},"attestation_state":"computed","paper":{"title":"Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Charles-Edouard Br\\'ehier, Erwan Faou","submitted_at":"2013-03-15T09:52:59Z","abstract_excerpt":"We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We study the Monte-Carlo error in a simple case, and show that under an anti-CFL condition on the time-step $\\delta t$ and on the mesh size $\\delta x$ and for $N$ - the number of realizations - reasonably large, we control this error by a term of order $\\mathcal{O}(\\sqrt{\\delta t /N})$. We also provide some numerical experiments to confirm the error estimate, and to expose some examples of equations which can be treated "},"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":"1303.3717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-03-15T09:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"918317ace71def0bf7c77730a3870430e4ea27c80f157abc4dc9dbb979b30128","abstract_canon_sha256":"b6964fe9d7abe1667e34ffaf18e546bce1619b966e513a342ad38b467d422587"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:52.628282Z","signature_b64":"yqhwGTo1cYXxtAviNS5XsE5SDPhHbqKC7+UcdH1028YmNCldzpF0I3r1qs1tbgyEwYNjm0JJDNddW0ItDisbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbd2f36bfb19aa231c91ff5c0df80c5c7c0b79f07916d5cf8a3a27da1a3751ad","last_reissued_at":"2026-05-18T03:30:52.627622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:52.627622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Charles-Edouard Br\\'ehier, Erwan Faou","submitted_at":"2013-03-15T09:52:59Z","abstract_excerpt":"We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We study the Monte-Carlo error in a simple case, and show that under an anti-CFL condition on the time-step $\\delta t$ and on the mesh size $\\delta x$ and for $N$ - the number of realizations - reasonably large, we control this error by a term of order $\\mathcal{O}(\\sqrt{\\delta t /N})$. We also provide some numerical experiments to confirm the error estimate, and to expose some examples of equations which can be treated "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3717","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":"1303.3717","created_at":"2026-05-18T03:30:52.627708+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3717v1","created_at":"2026-05-18T03:30:52.627708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3717","created_at":"2026-05-18T03:30:52.627708+00:00"},{"alias_kind":"pith_short_12","alias_value":"7PJPG273DGVC","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7PJPG273DGVCGHER","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7PJPG273","created_at":"2026-05-18T12:27:36.564083+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/7PJPG273DGVCGHER75OA36AMLR","json":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR.json","graph_json":"https://pith.science/api/pith-number/7PJPG273DGVCGHER75OA36AMLR/graph.json","events_json":"https://pith.science/api/pith-number/7PJPG273DGVCGHER75OA36AMLR/events.json","paper":"https://pith.science/paper/7PJPG273"},"agent_actions":{"view_html":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR","download_json":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR.json","view_paper":"https://pith.science/paper/7PJPG273","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3717&json=true","fetch_graph":"https://pith.science/api/pith-number/7PJPG273DGVCGHER75OA36AMLR/graph.json","fetch_events":"https://pith.science/api/pith-number/7PJPG273DGVCGHER75OA36AMLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR/action/storage_attestation","attest_author":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR/action/author_attestation","sign_citation":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR/action/citation_signature","submit_replication":"https://pith.science/pith/7PJPG273DGVCGHER75OA36AMLR/action/replication_record"}},"created_at":"2026-05-18T03:30:52.627708+00:00","updated_at":"2026-05-18T03:30:52.627708+00:00"}