{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EP5I7T5AN6KD4MGQHNN52JXVJE","short_pith_number":"pith:EP5I7T5A","schema_version":"1.0","canonical_sha256":"23fa8fcfa06f943e30d03b5bdd26f54900cb69fdef08a2a87d16993834cd87e3","source":{"kind":"arxiv","id":"1503.05290","version":1},"attestation_state":"computed","paper":{"title":"Convergence of Trimmed L\\'evy Processes to Trimmed Stable Random Variables at $0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuguang Fan","submitted_at":"2015-03-18T06:21:58Z","abstract_excerpt":"Let $^{(r,s)}X_t$ be the L\\'evy process $X_t$ with the $r$ largest jumps and $s$ smallest jumps up till time $t$ deleted and let $^{(r)}\\tilde X_t$ be $X_t$ with the $r$ largest jumps in modulus up till time $t$ deleted. We show that $({}^{(r,s)}X_t - a_t)/b_t$ or $({}^{(r)}\\tilde X_t - a_t)/b_t$ converges to a proper nondegenerate nonnormal limit distribution as $t \\downarrow 0$ if and only if $(X_t-a_t)/b_t $ converges as $t \\downarrow 0$ to an $\\alpha$-stable random variable, with $ 0 <\\alpha<2 $, where $a_t$ and $b_t>0$ are non stochastic functions in $t$. Together with the asymptotic norm"},"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":"1503.05290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T06:21:58Z","cross_cats_sorted":[],"title_canon_sha256":"36b05b69dacb53374bd4ed3343075114caa884ae00f380379584261ba58b16f2","abstract_canon_sha256":"73fe78f413344baa0c31be284245bfaf984099a084b260c5cde4f938fa61766b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:25.407239Z","signature_b64":"ruLPL937nhatYq0ir0pv0smO6OEm7glTOOubz7UcgTBgkawfpkEtL6tN22l0zRdRiEZJHtPmVz6tWfMi06pTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23fa8fcfa06f943e30d03b5bdd26f54900cb69fdef08a2a87d16993834cd87e3","last_reissued_at":"2026-05-18T01:26:25.406827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:25.406827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of Trimmed L\\'evy Processes to Trimmed Stable Random Variables at $0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuguang Fan","submitted_at":"2015-03-18T06:21:58Z","abstract_excerpt":"Let $^{(r,s)}X_t$ be the L\\'evy process $X_t$ with the $r$ largest jumps and $s$ smallest jumps up till time $t$ deleted and let $^{(r)}\\tilde X_t$ be $X_t$ with the $r$ largest jumps in modulus up till time $t$ deleted. We show that $({}^{(r,s)}X_t - a_t)/b_t$ or $({}^{(r)}\\tilde X_t - a_t)/b_t$ converges to a proper nondegenerate nonnormal limit distribution as $t \\downarrow 0$ if and only if $(X_t-a_t)/b_t $ converges as $t \\downarrow 0$ to an $\\alpha$-stable random variable, with $ 0 <\\alpha<2 $, where $a_t$ and $b_t>0$ are non stochastic functions in $t$. Together with the asymptotic norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05290","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":"1503.05290","created_at":"2026-05-18T01:26:25.406889+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.05290v1","created_at":"2026-05-18T01:26:25.406889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05290","created_at":"2026-05-18T01:26:25.406889+00:00"},{"alias_kind":"pith_short_12","alias_value":"EP5I7T5AN6KD","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EP5I7T5AN6KD4MGQ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EP5I7T5A","created_at":"2026-05-18T12:29:19.899920+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/EP5I7T5AN6KD4MGQHNN52JXVJE","json":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE.json","graph_json":"https://pith.science/api/pith-number/EP5I7T5AN6KD4MGQHNN52JXVJE/graph.json","events_json":"https://pith.science/api/pith-number/EP5I7T5AN6KD4MGQHNN52JXVJE/events.json","paper":"https://pith.science/paper/EP5I7T5A"},"agent_actions":{"view_html":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE","download_json":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE.json","view_paper":"https://pith.science/paper/EP5I7T5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.05290&json=true","fetch_graph":"https://pith.science/api/pith-number/EP5I7T5AN6KD4MGQHNN52JXVJE/graph.json","fetch_events":"https://pith.science/api/pith-number/EP5I7T5AN6KD4MGQHNN52JXVJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE/action/storage_attestation","attest_author":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE/action/author_attestation","sign_citation":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE/action/citation_signature","submit_replication":"https://pith.science/pith/EP5I7T5AN6KD4MGQHNN52JXVJE/action/replication_record"}},"created_at":"2026-05-18T01:26:25.406889+00:00","updated_at":"2026-05-18T01:26:25.406889+00:00"}