{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KNL37FTXOTXJKMSNBYUKO54YL6","short_pith_number":"pith:KNL37FTX","schema_version":"1.0","canonical_sha256":"5357bf967774ee95324d0e28a777985fafd9a4afa707e7231501bd1daf13a252","source":{"kind":"arxiv","id":"1610.04384","version":4},"attestation_state":"computed","paper":{"title":"Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erika Hausenblas, Hakima Bessaih, Paul A. Razafimandimby, Tsiry Randrianasolo","submitted_at":"2016-10-14T09:50:48Z","abstract_excerpt":"The present paper is devoted to the numerical approximation of an abstract stochastic nonlinear evolution equation in a separable Hilbert space {$\\mathrm{H}$}. Examples of equations which fall into our framework include the GOY and Sabra shell models and { a class of nonlinear heat equations.} The space-time numerical scheme is defined in terms of a Galerkin approximation in space and a { semi-implicit Euler--Maruyama scheme in time}. {We prove the convergence in probability of our scheme by means of an estimate of the error on a localized set of arbitrary large probability.} Our error estimat"},"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":"1610.04384","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-14T09:50:48Z","cross_cats_sorted":[],"title_canon_sha256":"1053484457b1f1a6d836e29ee34e8b2f74d631769fdc5771171cd1067a5c2274","abstract_canon_sha256":"1ea2a271b3c7570838c906107c2b1876525f88573b4975890eea19f5b7989b20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:41.966417Z","signature_b64":"8UNj897k3mJn6p4IgV4hUsrrUl/nhGrUnY/e+QhSH7C2HmT8l3eH4g6AJFFfTXXWvV92NS2EbWcCFcovNFWnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5357bf967774ee95324d0e28a777985fafd9a4afa707e7231501bd1daf13a252","last_reissued_at":"2026-05-18T00:04:41.965775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:41.965775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erika Hausenblas, Hakima Bessaih, Paul A. Razafimandimby, Tsiry Randrianasolo","submitted_at":"2016-10-14T09:50:48Z","abstract_excerpt":"The present paper is devoted to the numerical approximation of an abstract stochastic nonlinear evolution equation in a separable Hilbert space {$\\mathrm{H}$}. Examples of equations which fall into our framework include the GOY and Sabra shell models and { a class of nonlinear heat equations.} The space-time numerical scheme is defined in terms of a Galerkin approximation in space and a { semi-implicit Euler--Maruyama scheme in time}. {We prove the convergence in probability of our scheme by means of an estimate of the error on a localized set of arbitrary large probability.} Our error estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04384","kind":"arxiv","version":4},"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":"1610.04384","created_at":"2026-05-18T00:04:41.965880+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04384v4","created_at":"2026-05-18T00:04:41.965880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04384","created_at":"2026-05-18T00:04:41.965880+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNL37FTXOTXJ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNL37FTXOTXJKMSN","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNL37FTX","created_at":"2026-05-18T12:30:25.849896+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/KNL37FTXOTXJKMSNBYUKO54YL6","json":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6.json","graph_json":"https://pith.science/api/pith-number/KNL37FTXOTXJKMSNBYUKO54YL6/graph.json","events_json":"https://pith.science/api/pith-number/KNL37FTXOTXJKMSNBYUKO54YL6/events.json","paper":"https://pith.science/paper/KNL37FTX"},"agent_actions":{"view_html":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6","download_json":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6.json","view_paper":"https://pith.science/paper/KNL37FTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04384&json=true","fetch_graph":"https://pith.science/api/pith-number/KNL37FTXOTXJKMSNBYUKO54YL6/graph.json","fetch_events":"https://pith.science/api/pith-number/KNL37FTXOTXJKMSNBYUKO54YL6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/action/storage_attestation","attest_author":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/action/author_attestation","sign_citation":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/action/citation_signature","submit_replication":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/action/replication_record"}},"created_at":"2026-05-18T00:04:41.965880+00:00","updated_at":"2026-05-18T00:04:41.965880+00:00"}