{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GOLE7GQHY527BILOMSWD2YMMDX","short_pith_number":"pith:GOLE7GQH","schema_version":"1.0","canonical_sha256":"33964f9a07c775f0a16e64ac3d618c1decd4bc6c7076b9250fde4c6781ef7fd4","source":{"kind":"arxiv","id":"1103.3242","version":2},"attestation_state":"computed","paper":{"title":"Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florence Merlev\\`ede, Magda Peligrad","submitted_at":"2011-03-16T17:41:08Z","abstract_excerpt":"The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541-550] and Rio [J. Theoret. Probab. 22 (2009) 146-163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new maximal inequality generalizing the Doob maximal inequality for martingales and dyadic induction. Vari"},"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":"1103.3242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-16T17:41:08Z","cross_cats_sorted":[],"title_canon_sha256":"401520c2a94fdae2e87c0524a64be62b723133b37e74bdc425402e31ed7a987d","abstract_canon_sha256":"3623774e3337028365a56e276e98eff973e1af0c83ecc31b843aa521197bb660"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:42.587769Z","signature_b64":"EqoqC1YXnMdd4ZEy6v+Lp4NHBnvH3FSEBqZbWuuZFZeTzKgt+tRvRfJgQH4gxs6MzPCsTH7jMkPvc5UQSOn+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33964f9a07c775f0a16e64ac3d618c1decd4bc6c7076b9250fde4c6781ef7fd4","last_reissued_at":"2026-05-18T03:30:42.586979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:42.586979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florence Merlev\\`ede, Magda Peligrad","submitted_at":"2011-03-16T17:41:08Z","abstract_excerpt":"The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541-550] and Rio [J. Theoret. Probab. 22 (2009) 146-163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new maximal inequality generalizing the Doob maximal inequality for martingales and dyadic induction. Vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3242","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":"1103.3242","created_at":"2026-05-18T03:30:42.587110+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.3242v2","created_at":"2026-05-18T03:30:42.587110+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3242","created_at":"2026-05-18T03:30:42.587110+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOLE7GQHY527","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOLE7GQHY527BILO","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOLE7GQH","created_at":"2026-05-18T12:26:30.835961+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/GOLE7GQHY527BILOMSWD2YMMDX","json":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX.json","graph_json":"https://pith.science/api/pith-number/GOLE7GQHY527BILOMSWD2YMMDX/graph.json","events_json":"https://pith.science/api/pith-number/GOLE7GQHY527BILOMSWD2YMMDX/events.json","paper":"https://pith.science/paper/GOLE7GQH"},"agent_actions":{"view_html":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX","download_json":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX.json","view_paper":"https://pith.science/paper/GOLE7GQH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.3242&json=true","fetch_graph":"https://pith.science/api/pith-number/GOLE7GQHY527BILOMSWD2YMMDX/graph.json","fetch_events":"https://pith.science/api/pith-number/GOLE7GQHY527BILOMSWD2YMMDX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX/action/storage_attestation","attest_author":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX/action/author_attestation","sign_citation":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX/action/citation_signature","submit_replication":"https://pith.science/pith/GOLE7GQHY527BILOMSWD2YMMDX/action/replication_record"}},"created_at":"2026-05-18T03:30:42.587110+00:00","updated_at":"2026-05-18T03:30:42.587110+00:00"}