{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4ZKYZ72BMJH75FC7RM6PCMEQRJ","short_pith_number":"pith:4ZKYZ72B","schema_version":"1.0","canonical_sha256":"e6558cff41624ffe945f8b3cf130908a54b959532d7c44d1bc7d77749dc9333e","source":{"kind":"arxiv","id":"1403.1342","version":2},"attestation_state":"computed","paper":{"title":"Limit Theorems for Some Critical Superprocesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Rui Zhang, Yan-Xia Ren","submitted_at":"2014-03-06T04:25:41Z","abstract_excerpt":"In this paper we establish some conditional limit theorems for some critical superprocesses $X=\\{X_t, t\\ge 0\\}$. First we identify the rate of non-extinction. Then we show that, for a large class of functions $f$, conditioned on non-extinction at time $t$, the limit, as $t\\to\\infty$, of $t^{-1}\\langle f, X_t\\rangle$ exists in distribution and we identify this limit. Finally, we also establish, under some conditions, a central limit theorem for $\\langle f, X_t\\rangle$ conditioned on non-extinction at time $t$."},"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":"1403.1342","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-06T04:25:41Z","cross_cats_sorted":[],"title_canon_sha256":"07d3b90a704a018cb594f457c556c892a14565b7f8791910dba2f955a21abe42","abstract_canon_sha256":"5651ce6ac51015a0d4c341288f2b045872be1d3dc7980c201aab76f8e1fb83af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:11.039737Z","signature_b64":"CaKuoMG5tkKh62vZVm+N8vx8kOYAMhQ54w/NE8KgN71HTs12zbVEb3kU6u4MYK9Q5nEVe3PRWvImNriF3KhNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6558cff41624ffe945f8b3cf130908a54b959532d7c44d1bc7d77749dc9333e","last_reissued_at":"2026-05-18T01:26:11.039087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:11.039087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit Theorems for Some Critical Superprocesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Rui Zhang, Yan-Xia Ren","submitted_at":"2014-03-06T04:25:41Z","abstract_excerpt":"In this paper we establish some conditional limit theorems for some critical superprocesses $X=\\{X_t, t\\ge 0\\}$. First we identify the rate of non-extinction. Then we show that, for a large class of functions $f$, conditioned on non-extinction at time $t$, the limit, as $t\\to\\infty$, of $t^{-1}\\langle f, X_t\\rangle$ exists in distribution and we identify this limit. Finally, we also establish, under some conditions, a central limit theorem for $\\langle f, X_t\\rangle$ conditioned on non-extinction at time $t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1342","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":"1403.1342","created_at":"2026-05-18T01:26:11.039198+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.1342v2","created_at":"2026-05-18T01:26:11.039198+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1342","created_at":"2026-05-18T01:26:11.039198+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ZKYZ72BMJH7","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ZKYZ72BMJH75FC7","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ZKYZ72B","created_at":"2026-05-18T12:28:14.216126+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/4ZKYZ72BMJH75FC7RM6PCMEQRJ","json":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ.json","graph_json":"https://pith.science/api/pith-number/4ZKYZ72BMJH75FC7RM6PCMEQRJ/graph.json","events_json":"https://pith.science/api/pith-number/4ZKYZ72BMJH75FC7RM6PCMEQRJ/events.json","paper":"https://pith.science/paper/4ZKYZ72B"},"agent_actions":{"view_html":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ","download_json":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ.json","view_paper":"https://pith.science/paper/4ZKYZ72B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.1342&json=true","fetch_graph":"https://pith.science/api/pith-number/4ZKYZ72BMJH75FC7RM6PCMEQRJ/graph.json","fetch_events":"https://pith.science/api/pith-number/4ZKYZ72BMJH75FC7RM6PCMEQRJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ/action/storage_attestation","attest_author":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ/action/author_attestation","sign_citation":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ/action/citation_signature","submit_replication":"https://pith.science/pith/4ZKYZ72BMJH75FC7RM6PCMEQRJ/action/replication_record"}},"created_at":"2026-05-18T01:26:11.039198+00:00","updated_at":"2026-05-18T01:26:11.039198+00:00"}