{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:N74ZJ24MRMKR3N7GVRCAX6XHXF","short_pith_number":"pith:N74ZJ24M","schema_version":"1.0","canonical_sha256":"6ff994eb8c8b151db7e6ac440bfae7b943d24121b176bbed8fc9a81fa3490222","source":{"kind":"arxiv","id":"2204.04690","version":2},"attestation_state":"computed","paper":{"title":"Maximal Inequalities and Some Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Franziska K\\\"uhn, Ren\\'e L. Schilling","submitted_at":"2022-04-10T14:14:13Z","abstract_excerpt":"A maximal inequality is an inequality which involves the (absolute) supremum $\\sup_{s\\leq t}|X_{s}|$ or the running maximum $\\sup_{s\\leq t}X_{s}$ of a stochastic process $(X_t)_{t\\geq 0}$. We discuss maximal inequalities for several classes of stochastic processes with values in an Euclidean space: Martingales, L\\'evy processes, L\\'evy-type - including Feller processes, (compound) pseudo Poisson processes, stable-like processes and solutions to SDEs driven by a L\\'evy process -, strong Markov processes and Gaussian processes. Using the Burkholder-Davis-Gundy inequalities we als discuss some re"},"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":"2204.04690","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-04-10T14:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"d2465f01495cd020f0d48055cf514660e5abc791ff2c8918a545f73f0f0bf5c2","abstract_canon_sha256":"9bd03860baaea0d9ee9e51ee18f381bb8c408e6bec8d0cf4cfb8ba1659b75d70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:54:53.994057Z","signature_b64":"tY/1d5Jond9KmrpFltQjOtR+nbVu9IP87DE4ZSU3EZeOEDjfZb3mBPkrOxINpjDrhhwb6L9uAifh6Tj4BPIUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ff994eb8c8b151db7e6ac440bfae7b943d24121b176bbed8fc9a81fa3490222","last_reissued_at":"2026-07-05T05:54:53.993624Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:54:53.993624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal Inequalities and Some Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Franziska K\\\"uhn, Ren\\'e L. Schilling","submitted_at":"2022-04-10T14:14:13Z","abstract_excerpt":"A maximal inequality is an inequality which involves the (absolute) supremum $\\sup_{s\\leq t}|X_{s}|$ or the running maximum $\\sup_{s\\leq t}X_{s}$ of a stochastic process $(X_t)_{t\\geq 0}$. We discuss maximal inequalities for several classes of stochastic processes with values in an Euclidean space: Martingales, L\\'evy processes, L\\'evy-type - including Feller processes, (compound) pseudo Poisson processes, stable-like processes and solutions to SDEs driven by a L\\'evy process -, strong Markov processes and Gaussian processes. Using the Burkholder-Davis-Gundy inequalities we als discuss some re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.04690","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.04690/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2204.04690","created_at":"2026-07-05T05:54:53.993689+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.04690v2","created_at":"2026-07-05T05:54:53.993689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.04690","created_at":"2026-07-05T05:54:53.993689+00:00"},{"alias_kind":"pith_short_12","alias_value":"N74ZJ24MRMKR","created_at":"2026-07-05T05:54:53.993689+00:00"},{"alias_kind":"pith_short_16","alias_value":"N74ZJ24MRMKR3N7G","created_at":"2026-07-05T05:54:53.993689+00:00"},{"alias_kind":"pith_short_8","alias_value":"N74ZJ24M","created_at":"2026-07-05T05:54:53.993689+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/N74ZJ24MRMKR3N7GVRCAX6XHXF","json":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF.json","graph_json":"https://pith.science/api/pith-number/N74ZJ24MRMKR3N7GVRCAX6XHXF/graph.json","events_json":"https://pith.science/api/pith-number/N74ZJ24MRMKR3N7GVRCAX6XHXF/events.json","paper":"https://pith.science/paper/N74ZJ24M"},"agent_actions":{"view_html":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF","download_json":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF.json","view_paper":"https://pith.science/paper/N74ZJ24M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.04690&json=true","fetch_graph":"https://pith.science/api/pith-number/N74ZJ24MRMKR3N7GVRCAX6XHXF/graph.json","fetch_events":"https://pith.science/api/pith-number/N74ZJ24MRMKR3N7GVRCAX6XHXF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF/action/storage_attestation","attest_author":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF/action/author_attestation","sign_citation":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF/action/citation_signature","submit_replication":"https://pith.science/pith/N74ZJ24MRMKR3N7GVRCAX6XHXF/action/replication_record"}},"created_at":"2026-07-05T05:54:53.993689+00:00","updated_at":"2026-07-05T05:54:53.993689+00:00"}