{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:4I7SC4HQLN44RWVXPX7QMTAG3P","short_pith_number":"pith:4I7SC4HQ","schema_version":"1.0","canonical_sha256":"e23f2170f05b79c8dab77dff064c06dbca5abefdbf680f84d56f6dbbd384a852","source":{"kind":"arxiv","id":"1008.3221","version":1},"attestation_state":"computed","paper":{"title":"Pathwise Taylor Expansions for It\\^o Random Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ingo Bulla, Jin Ma, Rainer Buckdahn","submitted_at":"2010-08-19T06:12:52Z","abstract_excerpt":"In this paper we study the {\\it pathwise stochastic Taylor expansion}, in the sense of our previous work \\cite{Buckdahn_Ma_02}, for a class of It\\^o-type random fields in which the diffusion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an \"self-exciting\" type particularly contains the fully nonlinear stochastic PDEs of curvature driven diffusion, as well as certain stochastic Hamilton-Jacobi-Bellman equations. We introduce the new notion of \"$n$-fold\" derivatives of a random field, as a fundamental device to cope with the special se"},"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":"1008.3221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-19T06:12:52Z","cross_cats_sorted":[],"title_canon_sha256":"ef4ec39960f4bef271dadf6a46ac45ab3e14f8fe71dc74677661d1121ae405b0","abstract_canon_sha256":"a9653040ed06051e9dda353b003a1cc8d82403c39d5126903b1dd65153c6852a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:03.085968Z","signature_b64":"OD/zwiInJ7T8dO4bLUV91cdUBD0nHoTmm12TBsOn5YYtSmnZ6WNfb7MAMeUL82+Xp1AUj2K6uQ95h7xjTpoeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e23f2170f05b79c8dab77dff064c06dbca5abefdbf680f84d56f6dbbd384a852","last_reissued_at":"2026-05-18T04:42:03.085597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:03.085597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pathwise Taylor Expansions for It\\^o Random Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ingo Bulla, Jin Ma, Rainer Buckdahn","submitted_at":"2010-08-19T06:12:52Z","abstract_excerpt":"In this paper we study the {\\it pathwise stochastic Taylor expansion}, in the sense of our previous work \\cite{Buckdahn_Ma_02}, for a class of It\\^o-type random fields in which the diffusion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an \"self-exciting\" type particularly contains the fully nonlinear stochastic PDEs of curvature driven diffusion, as well as certain stochastic Hamilton-Jacobi-Bellman equations. We introduce the new notion of \"$n$-fold\" derivatives of a random field, as a fundamental device to cope with the special se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3221","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":"1008.3221","created_at":"2026-05-18T04:42:03.085662+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3221v1","created_at":"2026-05-18T04:42:03.085662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3221","created_at":"2026-05-18T04:42:03.085662+00:00"},{"alias_kind":"pith_short_12","alias_value":"4I7SC4HQLN44","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"4I7SC4HQLN44RWVX","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"4I7SC4HQ","created_at":"2026-05-18T12:26:03.138858+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/4I7SC4HQLN44RWVXPX7QMTAG3P","json":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P.json","graph_json":"https://pith.science/api/pith-number/4I7SC4HQLN44RWVXPX7QMTAG3P/graph.json","events_json":"https://pith.science/api/pith-number/4I7SC4HQLN44RWVXPX7QMTAG3P/events.json","paper":"https://pith.science/paper/4I7SC4HQ"},"agent_actions":{"view_html":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P","download_json":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P.json","view_paper":"https://pith.science/paper/4I7SC4HQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3221&json=true","fetch_graph":"https://pith.science/api/pith-number/4I7SC4HQLN44RWVXPX7QMTAG3P/graph.json","fetch_events":"https://pith.science/api/pith-number/4I7SC4HQLN44RWVXPX7QMTAG3P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P/action/storage_attestation","attest_author":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P/action/author_attestation","sign_citation":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P/action/citation_signature","submit_replication":"https://pith.science/pith/4I7SC4HQLN44RWVXPX7QMTAG3P/action/replication_record"}},"created_at":"2026-05-18T04:42:03.085662+00:00","updated_at":"2026-05-18T04:42:03.085662+00:00"}