{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GUI5YH4FDCW6BLKKNBQMZJ6AEB","short_pith_number":"pith:GUI5YH4F","schema_version":"1.0","canonical_sha256":"3511dc1f8518ade0ad4a6860cca7c02069384a5f939c37c8856a0396e022c730","source":{"kind":"arxiv","id":"1204.2946","version":2},"attestation_state":"computed","paper":{"title":"Tools for Malliavin calculus in UMD Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Mark Veraar, Matthijs Pronk","submitted_at":"2012-04-13T10:39:54Z","abstract_excerpt":"In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called UMD property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizatio"},"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":"1204.2946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-13T10:39:54Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c713202f2c93d9f8e24dd67a5dfd9d46d86c618097019f84049e538792fd83d2","abstract_canon_sha256":"0a28cb10f2066cbf1b5af54172b13f45fd8d9dae80b62decb06a258ee757847b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:14.727130Z","signature_b64":"jiXqPYdpeX7zGudvcv7ua1u9Xosw4HArxbHj+PWj0SlI6HTGW+kskeOcLZFSECOh3yqv9Cq1xZhn3KA8GJQSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3511dc1f8518ade0ad4a6860cca7c02069384a5f939c37c8856a0396e022c730","last_reissued_at":"2026-05-18T03:25:14.726470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:14.726470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tools for Malliavin calculus in UMD Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Mark Veraar, Matthijs Pronk","submitted_at":"2012-04-13T10:39:54Z","abstract_excerpt":"In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called UMD property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2946","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":"1204.2946","created_at":"2026-05-18T03:25:14.726601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2946v2","created_at":"2026-05-18T03:25:14.726601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2946","created_at":"2026-05-18T03:25:14.726601+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUI5YH4FDCW6","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUI5YH4FDCW6BLKK","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUI5YH4F","created_at":"2026-05-18T12:27:06.952714+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/GUI5YH4FDCW6BLKKNBQMZJ6AEB","json":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB.json","graph_json":"https://pith.science/api/pith-number/GUI5YH4FDCW6BLKKNBQMZJ6AEB/graph.json","events_json":"https://pith.science/api/pith-number/GUI5YH4FDCW6BLKKNBQMZJ6AEB/events.json","paper":"https://pith.science/paper/GUI5YH4F"},"agent_actions":{"view_html":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB","download_json":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB.json","view_paper":"https://pith.science/paper/GUI5YH4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2946&json=true","fetch_graph":"https://pith.science/api/pith-number/GUI5YH4FDCW6BLKKNBQMZJ6AEB/graph.json","fetch_events":"https://pith.science/api/pith-number/GUI5YH4FDCW6BLKKNBQMZJ6AEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB/action/storage_attestation","attest_author":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB/action/author_attestation","sign_citation":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB/action/citation_signature","submit_replication":"https://pith.science/pith/GUI5YH4FDCW6BLKKNBQMZJ6AEB/action/replication_record"}},"created_at":"2026-05-18T03:25:14.726601+00:00","updated_at":"2026-05-18T03:25:14.726601+00:00"}