{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ND4CTSHJOOOM2PWZP7LZUGGIVS","short_pith_number":"pith:ND4CTSHJ","schema_version":"1.0","canonical_sha256":"68f829c8e9739ccd3ed97fd79a18c8acaab8993cb8498aef0e57206cb177a630","source":{"kind":"arxiv","id":"1701.05680","version":3},"attestation_state":"computed","paper":{"title":"Strong Convergence Rate of Splitting Schemes for Stochastic Nonlinear Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Jialin Hong, Jianbo Cui, Weien Zhou, Zhihui Liu","submitted_at":"2017-01-20T04:13:44Z","abstract_excerpt":"We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schr\\\"odinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and exponential integrability of a sequence of splitting processes which are used to approximate the solution of the stochastic NLS equation. We show that the splitting processes converge to the solution with strong order $1/2$. Then we use the Crank--Nicolson scheme to temporally discretize the splitting process and get the temporal splitting scheme which also posses"},"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":"1701.05680","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-20T04:13:44Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a03e60ea80c91ed09e08a2317683e55d47843fb767b5d42de898f530d137a828","abstract_canon_sha256":"9a189662659bd6ea979670fdc48237df8ccd523212a6622f4b17f02974481ead"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:01.597644Z","signature_b64":"AlcyUSHDX7EcfLv6Lom9SPX4Bvc+ieGZyvdWV55lm0kCgvPCL5ll+bkmcgytnk7ucpHa/3iK7hE+N0Naiz9tCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68f829c8e9739ccd3ed97fd79a18c8acaab8993cb8498aef0e57206cb177a630","last_reissued_at":"2026-05-17T23:53:01.596997Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:01.596997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong Convergence Rate of Splitting Schemes for Stochastic Nonlinear Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Jialin Hong, Jianbo Cui, Weien Zhou, Zhihui Liu","submitted_at":"2017-01-20T04:13:44Z","abstract_excerpt":"We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schr\\\"odinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and exponential integrability of a sequence of splitting processes which are used to approximate the solution of the stochastic NLS equation. We show that the splitting processes converge to the solution with strong order $1/2$. Then we use the Crank--Nicolson scheme to temporally discretize the splitting process and get the temporal splitting scheme which also posses"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05680","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":"1701.05680","created_at":"2026-05-17T23:53:01.597107+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.05680v3","created_at":"2026-05-17T23:53:01.597107+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05680","created_at":"2026-05-17T23:53:01.597107+00:00"},{"alias_kind":"pith_short_12","alias_value":"ND4CTSHJOOOM","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"ND4CTSHJOOOM2PWZ","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"ND4CTSHJ","created_at":"2026-05-18T12:31:31.346846+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/ND4CTSHJOOOM2PWZP7LZUGGIVS","json":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS.json","graph_json":"https://pith.science/api/pith-number/ND4CTSHJOOOM2PWZP7LZUGGIVS/graph.json","events_json":"https://pith.science/api/pith-number/ND4CTSHJOOOM2PWZP7LZUGGIVS/events.json","paper":"https://pith.science/paper/ND4CTSHJ"},"agent_actions":{"view_html":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS","download_json":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS.json","view_paper":"https://pith.science/paper/ND4CTSHJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.05680&json=true","fetch_graph":"https://pith.science/api/pith-number/ND4CTSHJOOOM2PWZP7LZUGGIVS/graph.json","fetch_events":"https://pith.science/api/pith-number/ND4CTSHJOOOM2PWZP7LZUGGIVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/action/storage_attestation","attest_author":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/action/author_attestation","sign_citation":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/action/citation_signature","submit_replication":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/action/replication_record"}},"created_at":"2026-05-17T23:53:01.597107+00:00","updated_at":"2026-05-17T23:53:01.597107+00:00"}