{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CQS5PZ2FWXDMR4DCV7DYKM55UP","short_pith_number":"pith:CQS5PZ2F","schema_version":"1.0","canonical_sha256":"1425d7e745b5c6c8f062afc78533bda3dfe6f1d2dd7ba491df85e7f1f57f502b","source":{"kind":"arxiv","id":"1412.5032","version":3},"attestation_state":"computed","paper":{"title":"Almost automorphy and various extensions for stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Fazia Bedouhene (LMPA), Mannal Smaali (LMPA), Nouredine Challali (LMPA), Omar Mellah (LMPA), Paul Raynaud De Fitte (LMRS)","submitted_at":"2014-12-16T15:10:47Z","abstract_excerpt":"We compare different modes of pseudo almost automorphy and variants for stochastic processes: in probability, in quadratic mean, or in distribution in various senses. We show by a counterexample that square-mean (pseudo) almost automorphy is a property which is too strong for stochastic differential equations (SDEs). Finally, we consider two semilinear SDEs, one with almost automorphic coefficients and the second one with pseudo almost automorphic coefficients, and we prove the existence and uniqueness of a mild solution which is almost automorphic in distribution in the first case, and pseudo"},"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":"1412.5032","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-16T15:10:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"cdb9936a6a066dd3a96a0b83cee0b9d06b7ff744b199888627f36d599cc1f9d8","abstract_canon_sha256":"499730dae13806bef90f8636f9761de6814ccedf696129c94e79ac0c964de329"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:23.493211Z","signature_b64":"RBjI5zZxzwmQDxinPBFv+2GPDL7zjNrZtplRQt6lpNecIWXKI602AATHxKpYrFllZnWE63MCffl0AQM+afPeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1425d7e745b5c6c8f062afc78533bda3dfe6f1d2dd7ba491df85e7f1f57f502b","last_reissued_at":"2026-05-18T02:18:23.492657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:23.492657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost automorphy and various extensions for stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Fazia Bedouhene (LMPA), Mannal Smaali (LMPA), Nouredine Challali (LMPA), Omar Mellah (LMPA), Paul Raynaud De Fitte (LMRS)","submitted_at":"2014-12-16T15:10:47Z","abstract_excerpt":"We compare different modes of pseudo almost automorphy and variants for stochastic processes: in probability, in quadratic mean, or in distribution in various senses. We show by a counterexample that square-mean (pseudo) almost automorphy is a property which is too strong for stochastic differential equations (SDEs). Finally, we consider two semilinear SDEs, one with almost automorphic coefficients and the second one with pseudo almost automorphic coefficients, and we prove the existence and uniqueness of a mild solution which is almost automorphic in distribution in the first case, and pseudo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5032","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":"1412.5032","created_at":"2026-05-18T02:18:23.492736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5032v3","created_at":"2026-05-18T02:18:23.492736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5032","created_at":"2026-05-18T02:18:23.492736+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQS5PZ2FWXDM","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQS5PZ2FWXDMR4DC","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQS5PZ2F","created_at":"2026-05-18T12:28:22.404517+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/CQS5PZ2FWXDMR4DCV7DYKM55UP","json":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP.json","graph_json":"https://pith.science/api/pith-number/CQS5PZ2FWXDMR4DCV7DYKM55UP/graph.json","events_json":"https://pith.science/api/pith-number/CQS5PZ2FWXDMR4DCV7DYKM55UP/events.json","paper":"https://pith.science/paper/CQS5PZ2F"},"agent_actions":{"view_html":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP","download_json":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP.json","view_paper":"https://pith.science/paper/CQS5PZ2F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5032&json=true","fetch_graph":"https://pith.science/api/pith-number/CQS5PZ2FWXDMR4DCV7DYKM55UP/graph.json","fetch_events":"https://pith.science/api/pith-number/CQS5PZ2FWXDMR4DCV7DYKM55UP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP/action/storage_attestation","attest_author":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP/action/author_attestation","sign_citation":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP/action/citation_signature","submit_replication":"https://pith.science/pith/CQS5PZ2FWXDMR4DCV7DYKM55UP/action/replication_record"}},"created_at":"2026-05-18T02:18:23.492736+00:00","updated_at":"2026-05-18T02:18:23.492736+00:00"}