{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AWHBL3TC32N4MTIXYFSZ7KKWXB","short_pith_number":"pith:AWHBL3TC","schema_version":"1.0","canonical_sha256":"058e15ee62de9bc64d17c1659fa956b859421e129d742da3d8ed837edb6e92d1","source":{"kind":"arxiv","id":"1704.05577","version":1},"attestation_state":"computed","paper":{"title":"BMO estimates for stochastic singular integral operators and its application to PDEs with L\\'{e}vy noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangying Lv, Hongjun Gao, Jiang-Lun Wu, Jinlong Wei","submitted_at":"2017-04-19T01:57:44Z","abstract_excerpt":"In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises\n  \\bess du_t(x)=\\Delta^{\\frac{\\alpha}{2}}u_t(x)dt+\\sum_{k=1}^\\infty\\int_{\\mathbb{R}^m}g^k(t,x)z\\tilde N_k(dz,dt),\\ \\ \\ u_0=0,\\ 0\\leq t\\leq T,\n  \\eess where $\\Delta^{\\frac{\\alpha}{2}}=-(-\\Delta)^{\\frac{\\alpha}{2}}$, and $\\int_{\\mathbb{R}^m}z\\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump L\\'{e}vy processes with L\\'{e}vy measure of $\\nu^k$. Following the idea of \\cite{Kim}, we obtain the $q$-th"},"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":"1704.05577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T01:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"6cebea56bbacab30994634cf18c1639727e97cb857eadb478e35a4bfa49a2504","abstract_canon_sha256":"4e30f95e1d83ba034a7a9de417fc0d187b3e25e024940a7e0e0ebb127b329fed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:07.073258Z","signature_b64":"Zyxg4qaiOWZxG6Y9UuT4Fko3U6ncXdfuTf5yac7ftSxMEJ4dCyS+Zj3Ky0m/M//Gy/rUIte9QQwy3RGFHDOlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"058e15ee62de9bc64d17c1659fa956b859421e129d742da3d8ed837edb6e92d1","last_reissued_at":"2026-05-18T00:46:07.072706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:07.072706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"BMO estimates for stochastic singular integral operators and its application to PDEs with L\\'{e}vy noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangying Lv, Hongjun Gao, Jiang-Lun Wu, Jinlong Wei","submitted_at":"2017-04-19T01:57:44Z","abstract_excerpt":"In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises\n  \\bess du_t(x)=\\Delta^{\\frac{\\alpha}{2}}u_t(x)dt+\\sum_{k=1}^\\infty\\int_{\\mathbb{R}^m}g^k(t,x)z\\tilde N_k(dz,dt),\\ \\ \\ u_0=0,\\ 0\\leq t\\leq T,\n  \\eess where $\\Delta^{\\frac{\\alpha}{2}}=-(-\\Delta)^{\\frac{\\alpha}{2}}$, and $\\int_{\\mathbb{R}^m}z\\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump L\\'{e}vy processes with L\\'{e}vy measure of $\\nu^k$. Following the idea of \\cite{Kim}, we obtain the $q$-th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05577","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":""},"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":"1704.05577","created_at":"2026-05-18T00:46:07.072785+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.05577v1","created_at":"2026-05-18T00:46:07.072785+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05577","created_at":"2026-05-18T00:46:07.072785+00:00"},{"alias_kind":"pith_short_12","alias_value":"AWHBL3TC32N4","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"AWHBL3TC32N4MTIX","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"AWHBL3TC","created_at":"2026-05-18T12:31:08.081275+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/AWHBL3TC32N4MTIXYFSZ7KKWXB","json":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB.json","graph_json":"https://pith.science/api/pith-number/AWHBL3TC32N4MTIXYFSZ7KKWXB/graph.json","events_json":"https://pith.science/api/pith-number/AWHBL3TC32N4MTIXYFSZ7KKWXB/events.json","paper":"https://pith.science/paper/AWHBL3TC"},"agent_actions":{"view_html":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB","download_json":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB.json","view_paper":"https://pith.science/paper/AWHBL3TC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.05577&json=true","fetch_graph":"https://pith.science/api/pith-number/AWHBL3TC32N4MTIXYFSZ7KKWXB/graph.json","fetch_events":"https://pith.science/api/pith-number/AWHBL3TC32N4MTIXYFSZ7KKWXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/action/storage_attestation","attest_author":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/action/author_attestation","sign_citation":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/action/citation_signature","submit_replication":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/action/replication_record"}},"created_at":"2026-05-18T00:46:07.072785+00:00","updated_at":"2026-05-18T00:46:07.072785+00:00"}