{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SFLH63J7KDPVXZXFL3BHD4ZWWU","short_pith_number":"pith:SFLH63J7","schema_version":"1.0","canonical_sha256":"91567f6d3f50df5be6e55ec271f336b514bc2f092029abe0e8db726a1c89ebb4","source":{"kind":"arxiv","id":"1301.5715","version":2},"attestation_state":"computed","paper":{"title":"The covariation for Banach space valued processes and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cristina Di Girolami (LMM, DEA), Francesco Russo (UMA), Giorgio Fabbri (EPEE)","submitted_at":"2013-01-24T07:04:55Z","abstract_excerpt":"This article focuses on a new concept of quadratic variation for processes taking values in a Banach space $B$ and a corresponding covariation. This is more general than the classical one of M\\'etivier and Pellaumail. Those notions are associated with some subspace $\\chi$ of the dual of the projective tensor product of $B$ with itself. We also introduce the notion of a convolution type process, which is a natural generalization of the It\\^o process and the concept of $\\bar \\nu_0$-semimartingale, which is a natural extension of the classical notion of semimartingale. The framework is the stocha"},"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":"1301.5715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-24T07:04:55Z","cross_cats_sorted":[],"title_canon_sha256":"eef2d426e100805ae442841eca10484b024b16fb4468eb68f31839849b86a3c5","abstract_canon_sha256":"ee49ee3409d78dadd449140fdbb3963a65c97514d69b0bd5a6ce976dea3daecc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:00.223740Z","signature_b64":"A+11Jj+e+znqu7XhGNSHPFsvpxRF2QAOUKmUrdgu+fS41usTVlsWBF1G2FBArJSWjOwmy9l9EXJYBeTrcH4qAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91567f6d3f50df5be6e55ec271f336b514bc2f092029abe0e8db726a1c89ebb4","last_reissued_at":"2026-05-18T03:17:00.223217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:00.223217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The covariation for Banach space valued processes and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cristina Di Girolami (LMM, DEA), Francesco Russo (UMA), Giorgio Fabbri (EPEE)","submitted_at":"2013-01-24T07:04:55Z","abstract_excerpt":"This article focuses on a new concept of quadratic variation for processes taking values in a Banach space $B$ and a corresponding covariation. This is more general than the classical one of M\\'etivier and Pellaumail. Those notions are associated with some subspace $\\chi$ of the dual of the projective tensor product of $B$ with itself. We also introduce the notion of a convolution type process, which is a natural generalization of the It\\^o process and the concept of $\\bar \\nu_0$-semimartingale, which is a natural extension of the classical notion of semimartingale. The framework is the stocha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5715","kind":"arxiv","version":2},"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":"1301.5715","created_at":"2026-05-18T03:17:00.223293+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5715v2","created_at":"2026-05-18T03:17:00.223293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5715","created_at":"2026-05-18T03:17:00.223293+00:00"},{"alias_kind":"pith_short_12","alias_value":"SFLH63J7KDPV","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SFLH63J7KDPVXZXF","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SFLH63J7","created_at":"2026-05-18T12:27:59.945178+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/SFLH63J7KDPVXZXFL3BHD4ZWWU","json":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU.json","graph_json":"https://pith.science/api/pith-number/SFLH63J7KDPVXZXFL3BHD4ZWWU/graph.json","events_json":"https://pith.science/api/pith-number/SFLH63J7KDPVXZXFL3BHD4ZWWU/events.json","paper":"https://pith.science/paper/SFLH63J7"},"agent_actions":{"view_html":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU","download_json":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU.json","view_paper":"https://pith.science/paper/SFLH63J7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5715&json=true","fetch_graph":"https://pith.science/api/pith-number/SFLH63J7KDPVXZXFL3BHD4ZWWU/graph.json","fetch_events":"https://pith.science/api/pith-number/SFLH63J7KDPVXZXFL3BHD4ZWWU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU/action/storage_attestation","attest_author":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU/action/author_attestation","sign_citation":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU/action/citation_signature","submit_replication":"https://pith.science/pith/SFLH63J7KDPVXZXFL3BHD4ZWWU/action/replication_record"}},"created_at":"2026-05-18T03:17:00.223293+00:00","updated_at":"2026-05-18T03:17:00.223293+00:00"}