{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:UUIJVGO3576QCIWOSEW4Y6XFAJ","short_pith_number":"pith:UUIJVGO3","schema_version":"1.0","canonical_sha256":"a5109a99dbeffd0122ce912dcc7ae5025ea5eeea456e5697afc424fb10e84820","source":{"kind":"arxiv","id":"0912.0131","version":1},"attestation_state":"computed","paper":{"title":"Some applications of duality for L\\'evy processes in a half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"DMA), Jean Bertoin (PMA, Mladen Savov","submitted_at":"2009-12-01T12:04:23Z","abstract_excerpt":"The central result of this paper is an analytic duality relation for real-valued L\\'evy processes killed upon exiting a half-line. By Nagasawa's theorem, this yields a remarkable time-reversal identity involving the L\\'evy process conditioned to stay positive. As examples of applications, we construct a version of the L\\'evy process indexed by the entire real line and started from $-\\infty$ which enjoys a natural spatial-stationarity property, and point out that the latter leads to a natural Lamperti-type representation for self-similar Markov processes in $(0,\\infty)$ started from the entranc"},"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":"0912.0131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-01T12:04:23Z","cross_cats_sorted":[],"title_canon_sha256":"5540d3ff8329f7a490b6048eb7c348877a316d82af7756b397f172a168af4a5c","abstract_canon_sha256":"64c73ffae94f089261960f13d05e40e1a0a50fdb37cfee3f3ba14c603fe180c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:02.594881Z","signature_b64":"MwwLBNtkFDl3rrqCiUvtQfcEeW/T2xkFud4dutsNPvgtYZMiUZ5cLq7XtOXG2rx6WZlpqdu14kEIBiC6+1FrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5109a99dbeffd0122ce912dcc7ae5025ea5eeea456e5697afc424fb10e84820","last_reissued_at":"2026-05-18T02:58:02.594243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:02.594243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some applications of duality for L\\'evy processes in a half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"DMA), Jean Bertoin (PMA, Mladen Savov","submitted_at":"2009-12-01T12:04:23Z","abstract_excerpt":"The central result of this paper is an analytic duality relation for real-valued L\\'evy processes killed upon exiting a half-line. By Nagasawa's theorem, this yields a remarkable time-reversal identity involving the L\\'evy process conditioned to stay positive. As examples of applications, we construct a version of the L\\'evy process indexed by the entire real line and started from $-\\infty$ which enjoys a natural spatial-stationarity property, and point out that the latter leads to a natural Lamperti-type representation for self-similar Markov processes in $(0,\\infty)$ started from the entranc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0131","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":"0912.0131","created_at":"2026-05-18T02:58:02.594326+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.0131v1","created_at":"2026-05-18T02:58:02.594326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0131","created_at":"2026-05-18T02:58:02.594326+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUIJVGO3576Q","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUIJVGO3576QCIWO","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUIJVGO3","created_at":"2026-05-18T12:26:02.257875+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/UUIJVGO3576QCIWOSEW4Y6XFAJ","json":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ.json","graph_json":"https://pith.science/api/pith-number/UUIJVGO3576QCIWOSEW4Y6XFAJ/graph.json","events_json":"https://pith.science/api/pith-number/UUIJVGO3576QCIWOSEW4Y6XFAJ/events.json","paper":"https://pith.science/paper/UUIJVGO3"},"agent_actions":{"view_html":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ","download_json":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ.json","view_paper":"https://pith.science/paper/UUIJVGO3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.0131&json=true","fetch_graph":"https://pith.science/api/pith-number/UUIJVGO3576QCIWOSEW4Y6XFAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/UUIJVGO3576QCIWOSEW4Y6XFAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ/action/storage_attestation","attest_author":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ/action/author_attestation","sign_citation":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ/action/citation_signature","submit_replication":"https://pith.science/pith/UUIJVGO3576QCIWOSEW4Y6XFAJ/action/replication_record"}},"created_at":"2026-05-18T02:58:02.594326+00:00","updated_at":"2026-05-18T02:58:02.594326+00:00"}