{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HIJ3RK6IQCYQ52DUBWHU7RW6GG","short_pith_number":"pith:HIJ3RK6I","schema_version":"1.0","canonical_sha256":"3a13b8abc880b10ee8740d8f4fc6de318cc6e0f4e08e236313dfcc49e9972bb5","source":{"kind":"arxiv","id":"2411.09949","version":1},"attestation_state":"computed","paper":{"title":"$W_{\\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu, Peng Chen, XiaoLong Zhang, Xicheng Zhang","submitted_at":"2024-11-15T05:02:50Z","abstract_excerpt":"By establishing the regularity estimates for nonlocal Stein/Poisson equations under $\\gamma$-order H\\\"older and dissipative conditions on the coefficients, we derive the $W_{\\bf d}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $\\alpha$-stable noises with $\\alpha \\in (\\frac{1}{2}, 2)$, where $W_{\\bf d}$ denotes the Wasserstein metric with ${\\bf d}(x,y)=|x-y|^\\gamma\\wedge 1$ and $\\gamma \\in ((1-\\alpha)_+, 1]$."},"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":"2411.09949","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-15T05:02:50Z","cross_cats_sorted":[],"title_canon_sha256":"a8194939ae1e4a7bbcfa8730c2300d5edd3b37e4d9e0b8902277c7a0c8b8b48d","abstract_canon_sha256":"e1d7c7e150f491f9127da2d97460ef3a405d8c1c90c6f7eb9469d7a707a193ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:56.160751Z","signature_b64":"YP2MPTTzBzRPiKWvdtqHWZxdECyZB+8Q28AuhaQaWBIcf0sVO/57WSj0C7IKahiL34KjE+iltvt5Ro8zHDN9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a13b8abc880b10ee8740d8f4fc6de318cc6e0f4e08e236313dfcc49e9972bb5","last_reissued_at":"2026-07-05T09:35:56.160237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:56.160237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$W_{\\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu, Peng Chen, XiaoLong Zhang, Xicheng Zhang","submitted_at":"2024-11-15T05:02:50Z","abstract_excerpt":"By establishing the regularity estimates for nonlocal Stein/Poisson equations under $\\gamma$-order H\\\"older and dissipative conditions on the coefficients, we derive the $W_{\\bf d}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $\\alpha$-stable noises with $\\alpha \\in (\\frac{1}{2}, 2)$, where $W_{\\bf d}$ denotes the Wasserstein metric with ${\\bf d}(x,y)=|x-y|^\\gamma\\wedge 1$ and $\\gamma \\in ((1-\\alpha)_+, 1]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09949","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/2411.09949/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":"2411.09949","created_at":"2026-07-05T09:35:56.160299+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.09949v1","created_at":"2026-07-05T09:35:56.160299+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09949","created_at":"2026-07-05T09:35:56.160299+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIJ3RK6IQCYQ","created_at":"2026-07-05T09:35:56.160299+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIJ3RK6IQCYQ52DU","created_at":"2026-07-05T09:35:56.160299+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIJ3RK6I","created_at":"2026-07-05T09:35:56.160299+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/HIJ3RK6IQCYQ52DUBWHU7RW6GG","json":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG.json","graph_json":"https://pith.science/api/pith-number/HIJ3RK6IQCYQ52DUBWHU7RW6GG/graph.json","events_json":"https://pith.science/api/pith-number/HIJ3RK6IQCYQ52DUBWHU7RW6GG/events.json","paper":"https://pith.science/paper/HIJ3RK6I"},"agent_actions":{"view_html":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG","download_json":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG.json","view_paper":"https://pith.science/paper/HIJ3RK6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.09949&json=true","fetch_graph":"https://pith.science/api/pith-number/HIJ3RK6IQCYQ52DUBWHU7RW6GG/graph.json","fetch_events":"https://pith.science/api/pith-number/HIJ3RK6IQCYQ52DUBWHU7RW6GG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG/action/storage_attestation","attest_author":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG/action/author_attestation","sign_citation":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG/action/citation_signature","submit_replication":"https://pith.science/pith/HIJ3RK6IQCYQ52DUBWHU7RW6GG/action/replication_record"}},"created_at":"2026-07-05T09:35:56.160299+00:00","updated_at":"2026-07-05T09:35:56.160299+00:00"}