{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:LL5TR27ISRA72J3LX4GGAIH3YH","short_pith_number":"pith:LL5TR27I","schema_version":"1.0","canonical_sha256":"5afb38ebe89441fd276bbf0c6020fbc1ea95c214d54183b3d981f6f8d7919912","source":{"kind":"arxiv","id":"math/0607282","version":1},"attestation_state":"computed","paper":{"title":"Moment estimates for L\\'{e}vy Processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gilles Pag\\`es (PMA), Harald Luschgy","submitted_at":"2006-07-12T09:22:01Z","abstract_excerpt":"For real L\\'{e}vy processes $(X\\_t)\\_{t \\geq 0}$ having no Brownian component with Blumenthal-Getoor index $\\beta$, the estimate $\\E \\sup\\_{s \\leq t} | X\\_s - a\\_p s |^p \\leq C\\_p t$ for every $t \\in [0,1]$ and suitable $a\\_p \\in \\R$ has been established by Millar \\cite{MILL} for $\\beta < p \\leq 2$ provided $X\\_1 \\in L^p$. We derive extensions of these estimates to the cases $p > 2$ and $p \\leq\\beta$."},"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":"math/0607282","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-07-12T09:22:01Z","cross_cats_sorted":[],"title_canon_sha256":"5239f602b3abe0f3b46028c376bf7f55ec2a6dc398a71674d5c97c7132520b15","abstract_canon_sha256":"2294d96fce784c89996ad545f40ac4a1693375d08bec1261da44b15025f7f2a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:50.080550Z","signature_b64":"Iu11A/3gKwAu+a5N8gXB9Bvhn7JWOaF3Lxamosr5UW1x2iq6lHm8iqXdT1m/iILzzWOhdEOjy21XjqcFgxmlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5afb38ebe89441fd276bbf0c6020fbc1ea95c214d54183b3d981f6f8d7919912","last_reissued_at":"2026-05-18T01:08:50.079754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:50.079754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moment estimates for L\\'{e}vy Processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gilles Pag\\`es (PMA), Harald Luschgy","submitted_at":"2006-07-12T09:22:01Z","abstract_excerpt":"For real L\\'{e}vy processes $(X\\_t)\\_{t \\geq 0}$ having no Brownian component with Blumenthal-Getoor index $\\beta$, the estimate $\\E \\sup\\_{s \\leq t} | X\\_s - a\\_p s |^p \\leq C\\_p t$ for every $t \\in [0,1]$ and suitable $a\\_p \\in \\R$ has been established by Millar \\cite{MILL} for $\\beta < p \\leq 2$ provided $X\\_1 \\in L^p$. We derive extensions of these estimates to the cases $p > 2$ and $p \\leq\\beta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607282","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":"math/0607282","created_at":"2026-05-18T01:08:50.079890+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0607282v1","created_at":"2026-05-18T01:08:50.079890+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607282","created_at":"2026-05-18T01:08:50.079890+00:00"},{"alias_kind":"pith_short_12","alias_value":"LL5TR27ISRA7","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"LL5TR27ISRA72J3L","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"LL5TR27I","created_at":"2026-05-18T12:25:54.717736+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/LL5TR27ISRA72J3LX4GGAIH3YH","json":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH.json","graph_json":"https://pith.science/api/pith-number/LL5TR27ISRA72J3LX4GGAIH3YH/graph.json","events_json":"https://pith.science/api/pith-number/LL5TR27ISRA72J3LX4GGAIH3YH/events.json","paper":"https://pith.science/paper/LL5TR27I"},"agent_actions":{"view_html":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH","download_json":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH.json","view_paper":"https://pith.science/paper/LL5TR27I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0607282&json=true","fetch_graph":"https://pith.science/api/pith-number/LL5TR27ISRA72J3LX4GGAIH3YH/graph.json","fetch_events":"https://pith.science/api/pith-number/LL5TR27ISRA72J3LX4GGAIH3YH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH/action/storage_attestation","attest_author":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH/action/author_attestation","sign_citation":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH/action/citation_signature","submit_replication":"https://pith.science/pith/LL5TR27ISRA72J3LX4GGAIH3YH/action/replication_record"}},"created_at":"2026-05-18T01:08:50.079890+00:00","updated_at":"2026-05-18T01:08:50.079890+00:00"}