{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NF24MQJ5DM4KIF4L5BYELEPK5X","short_pith_number":"pith:NF24MQJ5","schema_version":"1.0","canonical_sha256":"6975c6413d1b38a4178be8704591eaedfafd7fb650f1d0bbbce193c5707d2890","source":{"kind":"arxiv","id":"1106.1976","version":2},"attestation_state":"computed","paper":{"title":"Stochastic Burgers PDEs with random coefficients and a generalization of the Cole-Hopf transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Athanasios Yannacopoulos, Nikolaos Englezos, Nikolaos Frangos, Xanthi-Isidora Kartala","submitted_at":"2011-06-10T08:31:17Z","abstract_excerpt":"This paper studies forward and backward versions of random Burgers equation (RBE) with stochastic coefficients. Firstly, the celebrated Cole-Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of FBSDEs. Exploiting this connection, we derive a generalization of the Cole-Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman-Kac representations for the solutions are provide"},"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":"1106.1976","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-10T08:31:17Z","cross_cats_sorted":[],"title_canon_sha256":"87e7ef7aa38406471d12d9ed6348afdba5e2222674aea149aee6506419b39798","abstract_canon_sha256":"d1f664dfddc58e8356c40f803c56477668707558e64da8c76f214425198941f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:45.210297Z","signature_b64":"ndOeDtdgwFbd3+5OSSfagb1ZSsA2VBQqwLBANd5Pwv7ubwCmdiDHbvzk6X2xl6joX+Ht/ZEwQLFM12Lc8WQdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6975c6413d1b38a4178be8704591eaedfafd7fb650f1d0bbbce193c5707d2890","last_reissued_at":"2026-05-18T03:31:45.209527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:45.209527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Burgers PDEs with random coefficients and a generalization of the Cole-Hopf transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Athanasios Yannacopoulos, Nikolaos Englezos, Nikolaos Frangos, Xanthi-Isidora Kartala","submitted_at":"2011-06-10T08:31:17Z","abstract_excerpt":"This paper studies forward and backward versions of random Burgers equation (RBE) with stochastic coefficients. Firstly, the celebrated Cole-Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of FBSDEs. Exploiting this connection, we derive a generalization of the Cole-Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman-Kac representations for the solutions are provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1976","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":"1106.1976","created_at":"2026-05-18T03:31:45.209637+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.1976v2","created_at":"2026-05-18T03:31:45.209637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1976","created_at":"2026-05-18T03:31:45.209637+00:00"},{"alias_kind":"pith_short_12","alias_value":"NF24MQJ5DM4K","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NF24MQJ5DM4KIF4L","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NF24MQJ5","created_at":"2026-05-18T12:26:37.096874+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/NF24MQJ5DM4KIF4L5BYELEPK5X","json":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X.json","graph_json":"https://pith.science/api/pith-number/NF24MQJ5DM4KIF4L5BYELEPK5X/graph.json","events_json":"https://pith.science/api/pith-number/NF24MQJ5DM4KIF4L5BYELEPK5X/events.json","paper":"https://pith.science/paper/NF24MQJ5"},"agent_actions":{"view_html":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X","download_json":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X.json","view_paper":"https://pith.science/paper/NF24MQJ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.1976&json=true","fetch_graph":"https://pith.science/api/pith-number/NF24MQJ5DM4KIF4L5BYELEPK5X/graph.json","fetch_events":"https://pith.science/api/pith-number/NF24MQJ5DM4KIF4L5BYELEPK5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X/action/storage_attestation","attest_author":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X/action/author_attestation","sign_citation":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X/action/citation_signature","submit_replication":"https://pith.science/pith/NF24MQJ5DM4KIF4L5BYELEPK5X/action/replication_record"}},"created_at":"2026-05-18T03:31:45.209637+00:00","updated_at":"2026-05-18T03:31:45.209637+00:00"}