{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JKIO53IANPZXQE34LDN5GJO544","short_pith_number":"pith:JKIO53IA","schema_version":"1.0","canonical_sha256":"4a90eeed006bf378137c58dbd325dde732fe5f8a44de2f318366440f7b7644d8","source":{"kind":"arxiv","id":"1610.08792","version":2},"attestation_state":"computed","paper":{"title":"Harnack inequalities and Bounds for Densities of Stochastic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gennaro Cibelli, Sergio Polidoro","submitted_at":"2016-10-27T14:17:13Z","abstract_excerpt":"We consider possibly degenerate parabolic operators in the form $$\n  \\sum_{k=1}^{m}X_{k}^{2}+X_{0}-\\partial_{t}, $$ that are naturally associated to a suitable family of stochastic differential equations, and satisfying the H\\\"ormander condition. Note that, under this assumption, the operators in the form $\\L$ has a smooth fundamental solution that agrees with the density of the corresponding stochastic process. We describe a method based on Harnack inequalities and on the construction of Harnack chains to prove lower bounds for the fundamental solution. We also briefly discuss PDE and SDE met"},"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":"1610.08792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-27T14:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"f005030a7e9728654626c25ba8057488c46e5e50211bf442f95cda3a78a81e77","abstract_canon_sha256":"d6afd5b53bf5a7e05680205add29bf114ba00648b196f84e72d5749485ad6906"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:30.100592Z","signature_b64":"VVN0JqoOsOwkTs1nzBctgwPPUWPlLR4MjK7zJSTVvLj4jfcEvV07qjswx7fy0gCOr6zFWk5nQeDS8iTQVRPeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a90eeed006bf378137c58dbd325dde732fe5f8a44de2f318366440f7b7644d8","last_reissued_at":"2026-05-18T00:51:30.100034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:30.100034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harnack inequalities and Bounds for Densities of Stochastic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gennaro Cibelli, Sergio Polidoro","submitted_at":"2016-10-27T14:17:13Z","abstract_excerpt":"We consider possibly degenerate parabolic operators in the form $$\n  \\sum_{k=1}^{m}X_{k}^{2}+X_{0}-\\partial_{t}, $$ that are naturally associated to a suitable family of stochastic differential equations, and satisfying the H\\\"ormander condition. Note that, under this assumption, the operators in the form $\\L$ has a smooth fundamental solution that agrees with the density of the corresponding stochastic process. We describe a method based on Harnack inequalities and on the construction of Harnack chains to prove lower bounds for the fundamental solution. We also briefly discuss PDE and SDE met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08792","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":"1610.08792","created_at":"2026-05-18T00:51:30.100118+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.08792v2","created_at":"2026-05-18T00:51:30.100118+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08792","created_at":"2026-05-18T00:51:30.100118+00:00"},{"alias_kind":"pith_short_12","alias_value":"JKIO53IANPZX","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JKIO53IANPZXQE34","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JKIO53IA","created_at":"2026-05-18T12:30:25.849896+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/JKIO53IANPZXQE34LDN5GJO544","json":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544.json","graph_json":"https://pith.science/api/pith-number/JKIO53IANPZXQE34LDN5GJO544/graph.json","events_json":"https://pith.science/api/pith-number/JKIO53IANPZXQE34LDN5GJO544/events.json","paper":"https://pith.science/paper/JKIO53IA"},"agent_actions":{"view_html":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544","download_json":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544.json","view_paper":"https://pith.science/paper/JKIO53IA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.08792&json=true","fetch_graph":"https://pith.science/api/pith-number/JKIO53IANPZXQE34LDN5GJO544/graph.json","fetch_events":"https://pith.science/api/pith-number/JKIO53IANPZXQE34LDN5GJO544/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544/action/storage_attestation","attest_author":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544/action/author_attestation","sign_citation":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544/action/citation_signature","submit_replication":"https://pith.science/pith/JKIO53IANPZXQE34LDN5GJO544/action/replication_record"}},"created_at":"2026-05-18T00:51:30.100118+00:00","updated_at":"2026-05-18T00:51:30.100118+00:00"}