{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NAY2VTSPQESLCPZBPAFKGEFAME","short_pith_number":"pith:NAY2VTSP","schema_version":"1.0","canonical_sha256":"6831aace4f8124b13f21780aa310a06123c1cf45140c96f1a3aceecca033b424","source":{"kind":"arxiv","id":"1410.5036","version":3},"attestation_state":"computed","paper":{"title":"Tightness and Convergence of Trimmed L\\'evy Processes to Normality at Small Times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuguang Fan","submitted_at":"2014-10-19T05:12:42Z","abstract_excerpt":"Let $^{(r,s)}X_t$ be the L\\'evy process $X_t$ with the $r$ largest positive jumps and $s$ smallest negative jumps up till time $t$ deleted and let $^{(r)}\\widetilde X_t$ be $X_t$ with the $r$ largest jumps in modulus up till time $t$ deleted. Let $a_t \\in \\mathbb{R}$ and $b_t>0$ be non-stochastic functions in $t$. We show that the tightness of $({}^{(r,s)}X_t - a_t)/b_t$ or $({}^{(r)}\\widetilde X_t - a_t)/b_t$ at $0$ implies the tightness of all normed ordered jumps, hence the tightness of the untrimmed process $(X_t -a_t)/b_t$ at $0$. We use this to deduce that the trimmed process $({}^{(r,s)"},"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":"1410.5036","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-19T05:12:42Z","cross_cats_sorted":[],"title_canon_sha256":"0f68473fb038ac359a6413cd5c039f11163e2d28052d3c5148ccfe39efc2b385","abstract_canon_sha256":"25181da1da1cc5c686c627759990d48b68f557db8819c9d70f4d51584dc87036"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:25.559088Z","signature_b64":"7vNqifS682U7+DIWTGHQ9Z/RwW8rvms7EtMhgFmwhPtDDjSmAbXeGus1rp2vIJRikwRGvxvVderofL7uaM7vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6831aace4f8124b13f21780aa310a06123c1cf45140c96f1a3aceecca033b424","last_reissued_at":"2026-05-18T01:26:25.558413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:25.558413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tightness and Convergence of Trimmed L\\'evy Processes to Normality at Small Times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuguang Fan","submitted_at":"2014-10-19T05:12:42Z","abstract_excerpt":"Let $^{(r,s)}X_t$ be the L\\'evy process $X_t$ with the $r$ largest positive jumps and $s$ smallest negative jumps up till time $t$ deleted and let $^{(r)}\\widetilde X_t$ be $X_t$ with the $r$ largest jumps in modulus up till time $t$ deleted. Let $a_t \\in \\mathbb{R}$ and $b_t>0$ be non-stochastic functions in $t$. We show that the tightness of $({}^{(r,s)}X_t - a_t)/b_t$ or $({}^{(r)}\\widetilde X_t - a_t)/b_t$ at $0$ implies the tightness of all normed ordered jumps, hence the tightness of the untrimmed process $(X_t -a_t)/b_t$ at $0$. We use this to deduce that the trimmed process $({}^{(r,s)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5036","kind":"arxiv","version":3},"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":"1410.5036","created_at":"2026-05-18T01:26:25.558498+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.5036v3","created_at":"2026-05-18T01:26:25.558498+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5036","created_at":"2026-05-18T01:26:25.558498+00:00"},{"alias_kind":"pith_short_12","alias_value":"NAY2VTSPQESL","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NAY2VTSPQESLCPZB","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NAY2VTSP","created_at":"2026-05-18T12:28:41.024544+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/NAY2VTSPQESLCPZBPAFKGEFAME","json":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME.json","graph_json":"https://pith.science/api/pith-number/NAY2VTSPQESLCPZBPAFKGEFAME/graph.json","events_json":"https://pith.science/api/pith-number/NAY2VTSPQESLCPZBPAFKGEFAME/events.json","paper":"https://pith.science/paper/NAY2VTSP"},"agent_actions":{"view_html":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME","download_json":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME.json","view_paper":"https://pith.science/paper/NAY2VTSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.5036&json=true","fetch_graph":"https://pith.science/api/pith-number/NAY2VTSPQESLCPZBPAFKGEFAME/graph.json","fetch_events":"https://pith.science/api/pith-number/NAY2VTSPQESLCPZBPAFKGEFAME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME/action/storage_attestation","attest_author":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME/action/author_attestation","sign_citation":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME/action/citation_signature","submit_replication":"https://pith.science/pith/NAY2VTSPQESLCPZBPAFKGEFAME/action/replication_record"}},"created_at":"2026-05-18T01:26:25.558498+00:00","updated_at":"2026-05-18T01:26:25.558498+00:00"}