{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZDMNPY7RGEW73P72CGA6NQO7HF","short_pith_number":"pith:ZDMNPY7R","schema_version":"1.0","canonical_sha256":"c8d8d7e3f1312dfdbffa1181e6c1df39737f4f9f467bd9f1f123045e4fe675f4","source":{"kind":"arxiv","id":"1209.1147","version":1},"attestation_state":"computed","paper":{"title":"Functional Convergence of Linear Sequences in a non-Skorokhod Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adam Jakubowski, Raluca Balan, Sana Louhichi","submitted_at":"2012-09-06T00:09:10Z","abstract_excerpt":"In this article, we prove a new functional limit theorem for the partial sum sequence $S_{[nt]}=\\sum_{i=1}^{[nt]}X_i$ corresponding to a linear sequence of the form $X_i=\\sum_{j \\in \\bZ}c_j \\xi_{i-j}$ with i.i.d. innovations $(\\xi_i)_{i \\in \\bZ}$ and real-valued coefficients $(c_j)_{j \\in \\bZ}$. This weak convergence result is obtained in space $\\bD[0,1]$ endowed with the $S$-topology introduced in Jakubowski (1992), and the limit process is a linear fractional stable motion (LFSM). One of our result provides an extension of the results of Avram and Taqqu (1992) to the case when the coefficien"},"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":"1209.1147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-06T00:09:10Z","cross_cats_sorted":[],"title_canon_sha256":"8add908ecec57777fb6fd8a23418b6e3b60ef8be684c5ca56fb67f1d2020e70c","abstract_canon_sha256":"028e9ba4c1b938f9ccf6b2ea42354df38628dace02af1cad7603c2169cc885db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:06.406249Z","signature_b64":"4UAGyFJla6Gsplgf6yMT4sd7seLs0kuDsHq6pLbpcK5UCEedkA+ZRr9Mped4Znec5Sb1OP8krNq/gTDSsM8ABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8d8d7e3f1312dfdbffa1181e6c1df39737f4f9f467bd9f1f123045e4fe675f4","last_reissued_at":"2026-05-18T03:46:06.405799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:06.405799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional Convergence of Linear Sequences in a non-Skorokhod Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adam Jakubowski, Raluca Balan, Sana Louhichi","submitted_at":"2012-09-06T00:09:10Z","abstract_excerpt":"In this article, we prove a new functional limit theorem for the partial sum sequence $S_{[nt]}=\\sum_{i=1}^{[nt]}X_i$ corresponding to a linear sequence of the form $X_i=\\sum_{j \\in \\bZ}c_j \\xi_{i-j}$ with i.i.d. innovations $(\\xi_i)_{i \\in \\bZ}$ and real-valued coefficients $(c_j)_{j \\in \\bZ}$. This weak convergence result is obtained in space $\\bD[0,1]$ endowed with the $S$-topology introduced in Jakubowski (1992), and the limit process is a linear fractional stable motion (LFSM). One of our result provides an extension of the results of Avram and Taqqu (1992) to the case when the coefficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1147","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":"1209.1147","created_at":"2026-05-18T03:46:06.405884+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.1147v1","created_at":"2026-05-18T03:46:06.405884+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1147","created_at":"2026-05-18T03:46:06.405884+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDMNPY7RGEW7","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDMNPY7RGEW73P72","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDMNPY7R","created_at":"2026-05-18T12:27:30.460161+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/ZDMNPY7RGEW73P72CGA6NQO7HF","json":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF.json","graph_json":"https://pith.science/api/pith-number/ZDMNPY7RGEW73P72CGA6NQO7HF/graph.json","events_json":"https://pith.science/api/pith-number/ZDMNPY7RGEW73P72CGA6NQO7HF/events.json","paper":"https://pith.science/paper/ZDMNPY7R"},"agent_actions":{"view_html":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF","download_json":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF.json","view_paper":"https://pith.science/paper/ZDMNPY7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.1147&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDMNPY7RGEW73P72CGA6NQO7HF/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDMNPY7RGEW73P72CGA6NQO7HF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF/action/storage_attestation","attest_author":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF/action/author_attestation","sign_citation":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF/action/citation_signature","submit_replication":"https://pith.science/pith/ZDMNPY7RGEW73P72CGA6NQO7HF/action/replication_record"}},"created_at":"2026-05-18T03:46:06.405884+00:00","updated_at":"2026-05-18T03:46:06.405884+00:00"}