{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V3LAS5XP4LEMVFJP5HQSKF2EAE","short_pith_number":"pith:V3LAS5XP","schema_version":"1.0","canonical_sha256":"aed60976efe2c8ca952fe9e12517440111cb8b8e4ecd9d6c7ec887e326465eee","source":{"kind":"arxiv","id":"1806.09763","version":1},"attestation_state":"computed","paper":{"title":"Small Time Convergence of Subordinators with Regularly or Slowly Varying Canonical Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross Maller, Tanja Schindler","submitted_at":"2018-06-26T02:24:48Z","abstract_excerpt":"We consider subordinators $X_\\alpha=(X_\\alpha(t))_{t\\ge 0}$ in the domain of attraction at 0 of a stable subordinator $(S_\\alpha(t))_{t\\ge 0}$ (where $\\alpha\\in(0,1)$); thus, with the property that $\\overline{\\Pi}_\\alpha$, the tail function of the canonical measure of $X_\\alpha$, is regularly varying of index $-\\alpha\\in (-1,0)$ as $x\\downarrow 0$. We also analyse the boundary case, $\\alpha=0$, when $\\overline{\\Pi}_\\alpha$ is slowly varying at 0. When $\\alpha\\in(0,1)$, we show that $(t \\overline{\\Pi}_\\alpha (X_\\alpha(t)))^{-1}$ converges in distribution, as $t\\downarrow 0$, to the random varia"},"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":"1806.09763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-26T02:24:48Z","cross_cats_sorted":[],"title_canon_sha256":"103add0232e93aec5fcd56946a4389902ed0fb0e539ad2b7ecbc3ae26aa1f40e","abstract_canon_sha256":"41ecfbc40109dc646d81ff266e930c365d59d532077aedbb33549b298d49080c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:23.443649Z","signature_b64":"lGZavmz3ay36jELdJ/Yi5IqVmii8R3iYDYdswVlCTO0ke5k2c94FDPc7X8aNuD5QejHvM0Nddy4GodhFAqIuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aed60976efe2c8ca952fe9e12517440111cb8b8e4ecd9d6c7ec887e326465eee","last_reissued_at":"2026-05-18T00:12:23.443030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:23.443030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small Time Convergence of Subordinators with Regularly or Slowly Varying Canonical Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross Maller, Tanja Schindler","submitted_at":"2018-06-26T02:24:48Z","abstract_excerpt":"We consider subordinators $X_\\alpha=(X_\\alpha(t))_{t\\ge 0}$ in the domain of attraction at 0 of a stable subordinator $(S_\\alpha(t))_{t\\ge 0}$ (where $\\alpha\\in(0,1)$); thus, with the property that $\\overline{\\Pi}_\\alpha$, the tail function of the canonical measure of $X_\\alpha$, is regularly varying of index $-\\alpha\\in (-1,0)$ as $x\\downarrow 0$. We also analyse the boundary case, $\\alpha=0$, when $\\overline{\\Pi}_\\alpha$ is slowly varying at 0. When $\\alpha\\in(0,1)$, we show that $(t \\overline{\\Pi}_\\alpha (X_\\alpha(t)))^{-1}$ converges in distribution, as $t\\downarrow 0$, to the random varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09763","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":"1806.09763","created_at":"2026-05-18T00:12:23.443131+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.09763v1","created_at":"2026-05-18T00:12:23.443131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09763","created_at":"2026-05-18T00:12:23.443131+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3LAS5XP4LEM","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3LAS5XP4LEMVFJP","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3LAS5XP","created_at":"2026-05-18T12:32:56.356000+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/V3LAS5XP4LEMVFJP5HQSKF2EAE","json":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE.json","graph_json":"https://pith.science/api/pith-number/V3LAS5XP4LEMVFJP5HQSKF2EAE/graph.json","events_json":"https://pith.science/api/pith-number/V3LAS5XP4LEMVFJP5HQSKF2EAE/events.json","paper":"https://pith.science/paper/V3LAS5XP"},"agent_actions":{"view_html":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE","download_json":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE.json","view_paper":"https://pith.science/paper/V3LAS5XP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.09763&json=true","fetch_graph":"https://pith.science/api/pith-number/V3LAS5XP4LEMVFJP5HQSKF2EAE/graph.json","fetch_events":"https://pith.science/api/pith-number/V3LAS5XP4LEMVFJP5HQSKF2EAE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE/action/storage_attestation","attest_author":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE/action/author_attestation","sign_citation":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE/action/citation_signature","submit_replication":"https://pith.science/pith/V3LAS5XP4LEMVFJP5HQSKF2EAE/action/replication_record"}},"created_at":"2026-05-18T00:12:23.443131+00:00","updated_at":"2026-05-18T00:12:23.443131+00:00"}