{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HTNWOP5ZLSHKWMUIFR4ODSA5DK","short_pith_number":"pith:HTNWOP5Z","schema_version":"1.0","canonical_sha256":"3cdb673fb95c8eab32882c78e1c81d1a941e132f98eb715bd67da92fa13067f0","source":{"kind":"arxiv","id":"1406.2581","version":3},"attestation_state":"computed","paper":{"title":"Multilevel path simulation for weak approximation schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.CP","authors_text":"Denis Belomestny, Tigran Nagapetyan","submitted_at":"2014-06-10T15:12:03Z","abstract_excerpt":"In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler scheme for L\\'evy driven stochastic differential equations, and show that, given a weak convergence of order $\\alpha\\geq 1/2,$ the complexity of the corresponding \"weak\" MLMC estimate is of order $\\varepsilon^{-2}\\log ^{2}(\\varepsilon).$ 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":"1406.2581","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2014-06-10T15:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"b5d2bd2b06d10e70398fe6148de19eb8eba28cb0f793ef17500f6766b8e2c8e7","abstract_canon_sha256":"fee25e4636b861e1882c638fd1ab12bc4df7ecc9ba06186bcc13b08b5991e877"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:03.493816Z","signature_b64":"GtA2cn0N2yBecDXDmzJPBSqpAH4ZPe4+wNjsvFjs5TYvegRikYT+269lrkDUKsUUdCIJHEDAxmVmB26QY04JDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cdb673fb95c8eab32882c78e1c81d1a941e132f98eb715bd67da92fa13067f0","last_reissued_at":"2026-05-18T02:41:03.493268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:03.493268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multilevel path simulation for weak approximation schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.CP","authors_text":"Denis Belomestny, Tigran Nagapetyan","submitted_at":"2014-06-10T15:12:03Z","abstract_excerpt":"In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler scheme for L\\'evy driven stochastic differential equations, and show that, given a weak convergence of order $\\alpha\\geq 1/2,$ the complexity of the corresponding \"weak\" MLMC estimate is of order $\\varepsilon^{-2}\\log ^{2}(\\varepsilon).$ T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2581","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":"1406.2581","created_at":"2026-05-18T02:41:03.493393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.2581v3","created_at":"2026-05-18T02:41:03.493393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2581","created_at":"2026-05-18T02:41:03.493393+00:00"},{"alias_kind":"pith_short_12","alias_value":"HTNWOP5ZLSHK","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HTNWOP5ZLSHKWMUI","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HTNWOP5Z","created_at":"2026-05-18T12:28:30.664211+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/HTNWOP5ZLSHKWMUIFR4ODSA5DK","json":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK.json","graph_json":"https://pith.science/api/pith-number/HTNWOP5ZLSHKWMUIFR4ODSA5DK/graph.json","events_json":"https://pith.science/api/pith-number/HTNWOP5ZLSHKWMUIFR4ODSA5DK/events.json","paper":"https://pith.science/paper/HTNWOP5Z"},"agent_actions":{"view_html":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK","download_json":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK.json","view_paper":"https://pith.science/paper/HTNWOP5Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.2581&json=true","fetch_graph":"https://pith.science/api/pith-number/HTNWOP5ZLSHKWMUIFR4ODSA5DK/graph.json","fetch_events":"https://pith.science/api/pith-number/HTNWOP5ZLSHKWMUIFR4ODSA5DK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK/action/storage_attestation","attest_author":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK/action/author_attestation","sign_citation":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK/action/citation_signature","submit_replication":"https://pith.science/pith/HTNWOP5ZLSHKWMUIFR4ODSA5DK/action/replication_record"}},"created_at":"2026-05-18T02:41:03.493393+00:00","updated_at":"2026-05-18T02:41:03.493393+00:00"}