{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZQLZGJJ4L2A37HCVW3X7SBTP2H","short_pith_number":"pith:ZQLZGJJ4","schema_version":"1.0","canonical_sha256":"cc1793253c5e81bf9c55b6eff9066fd1ee0112564bf59d5018d2cd43555f9ff4","source":{"kind":"arxiv","id":"1703.01095","version":2},"attestation_state":"computed","paper":{"title":"Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Arnaud Debussche (IRMAR, Charles-Edouard Br\\'ehier (ICJ, IPSO), PSPM)","submitted_at":"2017-03-03T10:02:15Z","abstract_excerpt":"We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or affine noise. The basic tool is a discrete version of a two sided stochastic integral which allows a new formulation for the derivatives of these solutions. We show that this can be used to generalize the weak order analysis performed in [16]. The tools we develop are very general and can be used to study many other examples of applications."},"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":"1703.01095","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-03T10:02:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"5ce390829cb20bb132885850693aefaa46e5217a7a37f410930bd63df530bb19","abstract_canon_sha256":"4f0ee5c9b18b2afbf33b432c4212690859ce0e863c17fb7b527949e99a4db81c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:01.262446Z","signature_b64":"9oWD8IAUhYp9OceSsxiD4HNF0VunI9+IqXB5Yfc7u3hCmNq5m1Z5aTPBt4xkYDw92fwetlCMBvTJtj0C64kADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc1793253c5e81bf9c55b6eff9066fd1ee0112564bf59d5018d2cd43555f9ff4","last_reissued_at":"2026-05-18T00:14:01.261849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:01.261849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Arnaud Debussche (IRMAR, Charles-Edouard Br\\'ehier (ICJ, IPSO), PSPM)","submitted_at":"2017-03-03T10:02:15Z","abstract_excerpt":"We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or affine noise. The basic tool is a discrete version of a two sided stochastic integral which allows a new formulation for the derivatives of these solutions. We show that this can be used to generalize the weak order analysis performed in [16]. The tools we develop are very general and can be used to study many other examples of applications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01095","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":"1703.01095","created_at":"2026-05-18T00:14:01.261924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.01095v2","created_at":"2026-05-18T00:14:01.261924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01095","created_at":"2026-05-18T00:14:01.261924+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQLZGJJ4L2A3","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQLZGJJ4L2A37HCV","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQLZGJJ4","created_at":"2026-05-18T12:31:59.375834+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/ZQLZGJJ4L2A37HCVW3X7SBTP2H","json":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H.json","graph_json":"https://pith.science/api/pith-number/ZQLZGJJ4L2A37HCVW3X7SBTP2H/graph.json","events_json":"https://pith.science/api/pith-number/ZQLZGJJ4L2A37HCVW3X7SBTP2H/events.json","paper":"https://pith.science/paper/ZQLZGJJ4"},"agent_actions":{"view_html":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H","download_json":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H.json","view_paper":"https://pith.science/paper/ZQLZGJJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.01095&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQLZGJJ4L2A37HCVW3X7SBTP2H/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQLZGJJ4L2A37HCVW3X7SBTP2H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H/action/storage_attestation","attest_author":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H/action/author_attestation","sign_citation":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H/action/citation_signature","submit_replication":"https://pith.science/pith/ZQLZGJJ4L2A37HCVW3X7SBTP2H/action/replication_record"}},"created_at":"2026-05-18T00:14:01.261924+00:00","updated_at":"2026-05-18T00:14:01.261924+00:00"}