{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GWXUJI7EV7WXD5POSZM6B7SSAR","short_pith_number":"pith:GWXUJI7E","schema_version":"1.0","canonical_sha256":"35af44a3e4afed71f5ee9659e0fe52044a17595b0ddcfe25467590297dee15bb","source":{"kind":"arxiv","id":"2505.12883","version":1},"attestation_state":"computed","paper":{"title":"Implicit numerical approximation for stochastic delay differential equations with the nonlinear diffusion term in the infinite horizon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Hongjiong Tian, Yudong Wang","submitted_at":"2025-05-19T09:11:44Z","abstract_excerpt":"This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by establishing the uniform moment boundedness and finite-time strong convergence of the BEM method, we prove that for sufficiently small step sizes, the numerical approximations strongly converge to the underlying solution in the infinite horizon with a rate of $1/2$, which coincides with the optimal finite-time strong convergence rate.\n  Next, we establish the un"},"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":"2505.12883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T09:11:44Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"ceaaac58fea6f2c6d892bbd892d935002b46a6e541f02f790dd9a34b34de9776","abstract_canon_sha256":"f067eccb68156e645ae69e5e9f339962005202dd0c7b87cb46f206522fb3d8e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:11.178049Z","signature_b64":"UC71AOt17qIVOf6wlwzOd++tvuvFeO7vXnnvFouDnpTuwXL794kYBtChac4/3Py29S298WwM8D8lF5G01GXZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35af44a3e4afed71f5ee9659e0fe52044a17595b0ddcfe25467590297dee15bb","last_reissued_at":"2026-07-05T11:05:11.177632Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:11.177632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Implicit numerical approximation for stochastic delay differential equations with the nonlinear diffusion term in the infinite horizon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Hongjiong Tian, Yudong Wang","submitted_at":"2025-05-19T09:11:44Z","abstract_excerpt":"This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by establishing the uniform moment boundedness and finite-time strong convergence of the BEM method, we prove that for sufficiently small step sizes, the numerical approximations strongly converge to the underlying solution in the infinite horizon with a rate of $1/2$, which coincides with the optimal finite-time strong convergence rate.\n  Next, we establish the un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12883","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.12883/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":"2505.12883","created_at":"2026-07-05T11:05:11.177694+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.12883v1","created_at":"2026-07-05T11:05:11.177694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12883","created_at":"2026-07-05T11:05:11.177694+00:00"},{"alias_kind":"pith_short_12","alias_value":"GWXUJI7EV7WX","created_at":"2026-07-05T11:05:11.177694+00:00"},{"alias_kind":"pith_short_16","alias_value":"GWXUJI7EV7WXD5PO","created_at":"2026-07-05T11:05:11.177694+00:00"},{"alias_kind":"pith_short_8","alias_value":"GWXUJI7E","created_at":"2026-07-05T11:05:11.177694+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/GWXUJI7EV7WXD5POSZM6B7SSAR","json":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR.json","graph_json":"https://pith.science/api/pith-number/GWXUJI7EV7WXD5POSZM6B7SSAR/graph.json","events_json":"https://pith.science/api/pith-number/GWXUJI7EV7WXD5POSZM6B7SSAR/events.json","paper":"https://pith.science/paper/GWXUJI7E"},"agent_actions":{"view_html":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR","download_json":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR.json","view_paper":"https://pith.science/paper/GWXUJI7E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.12883&json=true","fetch_graph":"https://pith.science/api/pith-number/GWXUJI7EV7WXD5POSZM6B7SSAR/graph.json","fetch_events":"https://pith.science/api/pith-number/GWXUJI7EV7WXD5POSZM6B7SSAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR/action/storage_attestation","attest_author":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR/action/author_attestation","sign_citation":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR/action/citation_signature","submit_replication":"https://pith.science/pith/GWXUJI7EV7WXD5POSZM6B7SSAR/action/replication_record"}},"created_at":"2026-07-05T11:05:11.177694+00:00","updated_at":"2026-07-05T11:05:11.177694+00:00"}