{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7QJ3FAO43E2NYRIX53VXM5YEZQ","short_pith_number":"pith:7QJ3FAO4","schema_version":"1.0","canonical_sha256":"fc13b281dcd934dc4517eeeb767704cc2e8c0e40e859559fc35185b7f5e75bf7","source":{"kind":"arxiv","id":"1104.1064","version":1},"attestation_state":"computed","paper":{"title":"Limit theorems for power variations of pure-jump processes with application to activity estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"George Tauchen, Viktor Todorov","submitted_at":"2011-04-06T11:29:07Z","abstract_excerpt":"This paper derives the asymptotic behavior of realized power variation of pure-jump It\\^{o} semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an efficient adaptive estimator for the activity of discretely-sampled It\\^{o} semimartingale over a fixed interval."},"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":"1104.1064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-06T11:29:07Z","cross_cats_sorted":[],"title_canon_sha256":"c8674478dcd273998da71b59102d395ffab4db598c7cb704bb4c110be706ad7a","abstract_canon_sha256":"53ef036c0fe6fc344d982fcad2556085409c82cf0c1e28511727a6d82b2f2a37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:53.708504Z","signature_b64":"fdDVChSpMbBcbEZO/Eq0Ayd7ebb0v0oWELRZRnrMSrw7jAteDLbLFarX6b9YESoqKa8bcQe2l7xQni+znLMvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc13b281dcd934dc4517eeeb767704cc2e8c0e40e859559fc35185b7f5e75bf7","last_reissued_at":"2026-05-18T04:24:53.707929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:53.707929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit theorems for power variations of pure-jump processes with application to activity estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"George Tauchen, Viktor Todorov","submitted_at":"2011-04-06T11:29:07Z","abstract_excerpt":"This paper derives the asymptotic behavior of realized power variation of pure-jump It\\^{o} semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an efficient adaptive estimator for the activity of discretely-sampled It\\^{o} semimartingale over a fixed interval."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1064","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":"1104.1064","created_at":"2026-05-18T04:24:53.708032+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.1064v1","created_at":"2026-05-18T04:24:53.708032+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1064","created_at":"2026-05-18T04:24:53.708032+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QJ3FAO43E2N","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QJ3FAO43E2NYRIX","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QJ3FAO4","created_at":"2026-05-18T12:26:22.705136+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/7QJ3FAO43E2NYRIX53VXM5YEZQ","json":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ.json","graph_json":"https://pith.science/api/pith-number/7QJ3FAO43E2NYRIX53VXM5YEZQ/graph.json","events_json":"https://pith.science/api/pith-number/7QJ3FAO43E2NYRIX53VXM5YEZQ/events.json","paper":"https://pith.science/paper/7QJ3FAO4"},"agent_actions":{"view_html":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ","download_json":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ.json","view_paper":"https://pith.science/paper/7QJ3FAO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.1064&json=true","fetch_graph":"https://pith.science/api/pith-number/7QJ3FAO43E2NYRIX53VXM5YEZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/7QJ3FAO43E2NYRIX53VXM5YEZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ/action/storage_attestation","attest_author":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ/action/author_attestation","sign_citation":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ/action/citation_signature","submit_replication":"https://pith.science/pith/7QJ3FAO43E2NYRIX53VXM5YEZQ/action/replication_record"}},"created_at":"2026-05-18T04:24:53.708032+00:00","updated_at":"2026-05-18T04:24:53.708032+00:00"}