{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2P5C3AXMO7FTKTWS7E6AMUA6VK","short_pith_number":"pith:2P5C3AXM","schema_version":"1.0","canonical_sha256":"d3fa2d82ec77cb354ed2f93c06501eaa9d682cc2e3871a948c3c7fc293aded92","source":{"kind":"arxiv","id":"1707.01116","version":1},"attestation_state":"computed","paper":{"title":"Heavy-tailed fractional Pearson diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alla Sikorskii, Ivan Papi\\'c, Nenad \\v{S}uvak, Nikolai N. Leonenko","submitted_at":"2017-07-04T18:04:53Z","abstract_excerpt":"We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal "},"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":"1707.01116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-04T18:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"10ae0986f2cc4040d75c776f2385ad9e03f2bfc8b60bbda4cefdce2cd1a46cf3","abstract_canon_sha256":"02c8d25bcd18eabdc6c1cb26df9fe4e5d8817ec1a6b057a1fc768e69dbfae62b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.626226Z","signature_b64":"QYi+O52mFto2rY7/Nk9RJD17uxZc8Dyv5zMsxpARhr9RWKcMapfsyLRLAuOiwCUlkBzUZFKegXak6y2dahD0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3fa2d82ec77cb354ed2f93c06501eaa9d682cc2e3871a948c3c7fc293aded92","last_reissued_at":"2026-05-18T00:40:53.625838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.625838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heavy-tailed fractional Pearson diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alla Sikorskii, Ivan Papi\\'c, Nenad \\v{S}uvak, Nikolai N. Leonenko","submitted_at":"2017-07-04T18:04:53Z","abstract_excerpt":"We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01116","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":"1707.01116","created_at":"2026-05-18T00:40:53.625897+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01116v1","created_at":"2026-05-18T00:40:53.625897+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01116","created_at":"2026-05-18T00:40:53.625897+00:00"},{"alias_kind":"pith_short_12","alias_value":"2P5C3AXMO7FT","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2P5C3AXMO7FTKTWS","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2P5C3AXM","created_at":"2026-05-18T12:30:55.937587+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/2P5C3AXMO7FTKTWS7E6AMUA6VK","json":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK.json","graph_json":"https://pith.science/api/pith-number/2P5C3AXMO7FTKTWS7E6AMUA6VK/graph.json","events_json":"https://pith.science/api/pith-number/2P5C3AXMO7FTKTWS7E6AMUA6VK/events.json","paper":"https://pith.science/paper/2P5C3AXM"},"agent_actions":{"view_html":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK","download_json":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK.json","view_paper":"https://pith.science/paper/2P5C3AXM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01116&json=true","fetch_graph":"https://pith.science/api/pith-number/2P5C3AXMO7FTKTWS7E6AMUA6VK/graph.json","fetch_events":"https://pith.science/api/pith-number/2P5C3AXMO7FTKTWS7E6AMUA6VK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK/action/storage_attestation","attest_author":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK/action/author_attestation","sign_citation":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK/action/citation_signature","submit_replication":"https://pith.science/pith/2P5C3AXMO7FTKTWS7E6AMUA6VK/action/replication_record"}},"created_at":"2026-05-18T00:40:53.625897+00:00","updated_at":"2026-05-18T00:40:53.625897+00:00"}