{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:I2KJXE2JKF254KU7XHEYPF7VS5","short_pith_number":"pith:I2KJXE2J","schema_version":"1.0","canonical_sha256":"46949b93495175de2a9fb9c98797f59749ea0af1fd54d6dbe6c88e2ad25d52a0","source":{"kind":"arxiv","id":"1608.03766","version":1},"attestation_state":"computed","paper":{"title":"Construction of a surface integral under local Malliavin assumption and integration by parts formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Giuseppe Da Prato, Luciano Tubaro, Stefano Bonaccorsi","submitted_at":"2016-08-12T12:08:21Z","abstract_excerpt":"In this paper, we consider convex sets $K_r = \\{g \\ge r\\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $\\mu$ in $H$. We first show how to define a surface measure on the level sets $\\{g = r\\}$ that is related to $\\mu$. This allows to introduce an integration-by-parts formula in $H$. This formula can be applied in several important constructions, as for instance the case where $\\mu$ is the law of a (Gaussian) stochastic process and $H$ is the space of its trajectories"},"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":"1608.03766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T12:08:21Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"444df325fcd97698746fd6e450a4676637cc47026df3621b8347c63450d960cc","abstract_canon_sha256":"0a2183bb30035c5d536779ffdd0a5856d546394a6733af5ee316df15d4c29232"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:33.128858Z","signature_b64":"jC5S5IEzkT9SwLXsMBk3bj0IOmwQF9zTUiRXO09jN2aOmVhXLfa2ymrQdLiC/YG8uf61OKrGofVOwa1MS4/vBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46949b93495175de2a9fb9c98797f59749ea0af1fd54d6dbe6c88e2ad25d52a0","last_reissued_at":"2026-05-17T23:57:33.128464Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:33.128464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of a surface integral under local Malliavin assumption and integration by parts formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Giuseppe Da Prato, Luciano Tubaro, Stefano Bonaccorsi","submitted_at":"2016-08-12T12:08:21Z","abstract_excerpt":"In this paper, we consider convex sets $K_r = \\{g \\ge r\\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $\\mu$ in $H$. We first show how to define a surface measure on the level sets $\\{g = r\\}$ that is related to $\\mu$. This allows to introduce an integration-by-parts formula in $H$. This formula can be applied in several important constructions, as for instance the case where $\\mu$ is the law of a (Gaussian) stochastic process and $H$ is the space of its trajectories"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03766","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":"1608.03766","created_at":"2026-05-17T23:57:33.128516+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03766v1","created_at":"2026-05-17T23:57:33.128516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03766","created_at":"2026-05-17T23:57:33.128516+00:00"},{"alias_kind":"pith_short_12","alias_value":"I2KJXE2JKF25","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"I2KJXE2JKF254KU7","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"I2KJXE2J","created_at":"2026-05-18T12:30:22.444734+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/I2KJXE2JKF254KU7XHEYPF7VS5","json":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5.json","graph_json":"https://pith.science/api/pith-number/I2KJXE2JKF254KU7XHEYPF7VS5/graph.json","events_json":"https://pith.science/api/pith-number/I2KJXE2JKF254KU7XHEYPF7VS5/events.json","paper":"https://pith.science/paper/I2KJXE2J"},"agent_actions":{"view_html":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5","download_json":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5.json","view_paper":"https://pith.science/paper/I2KJXE2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03766&json=true","fetch_graph":"https://pith.science/api/pith-number/I2KJXE2JKF254KU7XHEYPF7VS5/graph.json","fetch_events":"https://pith.science/api/pith-number/I2KJXE2JKF254KU7XHEYPF7VS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/action/storage_attestation","attest_author":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/action/author_attestation","sign_citation":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/action/citation_signature","submit_replication":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/action/replication_record"}},"created_at":"2026-05-17T23:57:33.128516+00:00","updated_at":"2026-05-17T23:57:33.128516+00:00"}