{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:H6XM2YRXQVELCZNSRGM4GYNIS4","short_pith_number":"pith:H6XM2YRX","schema_version":"1.0","canonical_sha256":"3faecd62378548b165b28999c361a8972ecaae8ab7e3f02a56762cf37bda14f9","source":{"kind":"arxiv","id":"1512.05317","version":2},"attestation_state":"computed","paper":{"title":"Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Andreas Petersson, Annika Lang","submitted_at":"2015-12-16T20:22:17Z","abstract_excerpt":"The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a stochastic partial differential equation. If the convergence of Y_n to Y in terms of the error |E[Y - Y_n]| is to be simulated, this will typically be done by a Monte Carlo method, i.e., |E[Y] - E_N[Y_n]| is computed. In this article upper and lower bounds for the additional error caused by this are determined and compared to those of |E_N[Y - Y_n]|, which "},"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":"1512.05317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-16T20:22:17Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"1aeecede4813bb434879db92306022c7ed0901420eaedb7d155268c3f11561bc","abstract_canon_sha256":"809f947db0a91931c488e79c3ec97d1554e582ca9cf3a1bdf360f961ee75d206"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T17:09:49.797573Z","signature_b64":"PAQ0MLw5ha6HkgEFVnpxyoRVBLjZSJnWDzygt4rH6mjg7+5dEv4AqunSvtoe7i3axSdBrfp/p+N7hlh9dzeLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3faecd62378548b165b28999c361a8972ecaae8ab7e3f02a56762cf37bda14f9","last_reissued_at":"2026-06-04T17:09:49.797089Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T17:09:49.797089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Andreas Petersson, Annika Lang","submitted_at":"2015-12-16T20:22:17Z","abstract_excerpt":"The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a stochastic partial differential equation. If the convergence of Y_n to Y in terms of the error |E[Y - Y_n]| is to be simulated, this will typically be done by a Monte Carlo method, i.e., |E[Y] - E_N[Y_n]| is computed. In this article upper and lower bounds for the additional error caused by this are determined and compared to those of |E_N[Y - Y_n]|, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05317","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1512.05317/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1512.05317","created_at":"2026-06-04T17:09:49.797144+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.05317v2","created_at":"2026-06-04T17:09:49.797144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05317","created_at":"2026-06-04T17:09:49.797144+00:00"},{"alias_kind":"pith_short_12","alias_value":"H6XM2YRXQVEL","created_at":"2026-06-04T17:09:49.797144+00:00"},{"alias_kind":"pith_short_16","alias_value":"H6XM2YRXQVELCZNS","created_at":"2026-06-04T17:09:49.797144+00:00"},{"alias_kind":"pith_short_8","alias_value":"H6XM2YRX","created_at":"2026-06-04T17:09:49.797144+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/H6XM2YRXQVELCZNSRGM4GYNIS4","json":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4.json","graph_json":"https://pith.science/api/pith-number/H6XM2YRXQVELCZNSRGM4GYNIS4/graph.json","events_json":"https://pith.science/api/pith-number/H6XM2YRXQVELCZNSRGM4GYNIS4/events.json","paper":"https://pith.science/paper/H6XM2YRX"},"agent_actions":{"view_html":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4","download_json":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4.json","view_paper":"https://pith.science/paper/H6XM2YRX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.05317&json=true","fetch_graph":"https://pith.science/api/pith-number/H6XM2YRXQVELCZNSRGM4GYNIS4/graph.json","fetch_events":"https://pith.science/api/pith-number/H6XM2YRXQVELCZNSRGM4GYNIS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4/action/storage_attestation","attest_author":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4/action/author_attestation","sign_citation":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4/action/citation_signature","submit_replication":"https://pith.science/pith/H6XM2YRXQVELCZNSRGM4GYNIS4/action/replication_record"}},"created_at":"2026-06-04T17:09:49.797144+00:00","updated_at":"2026-06-04T17:09:49.797144+00:00"}