{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:25E5LQDA7OE2JONMSYJV3PD2EV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"64471b82ce6df9a4ddaf4fca2941069f482340f3b3f3bf74c2db3d895c898141","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-25T07:11:54Z","title_canon_sha256":"3e5167d7dbb75f9cac9fb81a3a96502ee2e6f87eb127e43608bdbd19d0c0f6fc"},"schema_version":"1.0","source":{"id":"1207.5902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5902","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5902v1","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5902","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"25E5LQDA7OE2","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"25E5LQDA7OE2JONM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"25E5LQDA","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:8c8a0337fcd76b812f6970ef37ed44e8c1b62f02df7eba293cd3f8465210c529","target":"graph","created_at":"2026-05-18T03:50:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove several results on the behavior near t=0 of $Y_t^{-t}$ for certain $(0,\\infty)$-valued stochastic processes $(Y_t)_{t>0}$. In particular, we show for L\\'{e}vy subordinators that the Pareto law on $[1,\\infty)$ is the only possible weak limit and provide necessary and sufficient conditions for the convergence. More generally, we also consider the weak convergence of $tL(Y_t)$ as $t\\to0$ for a decreasing function $L$ that is slowly varying at zero. Various examples demonstrating the applicability of the results are presented.","authors_text":"Andreas L\\\"opker, Shaul K. Bar-Lev, Wolfgang Stadje","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-25T07:11:54Z","title":"On the small-time behavior of subordinators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5902","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3451ebdae0bcf6a45e02c06cd30b5b3f7fc121cc297bf76676a014ca2be80ea7","target":"record","created_at":"2026-05-18T03:50:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"64471b82ce6df9a4ddaf4fca2941069f482340f3b3f3bf74c2db3d895c898141","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-25T07:11:54Z","title_canon_sha256":"3e5167d7dbb75f9cac9fb81a3a96502ee2e6f87eb127e43608bdbd19d0c0f6fc"},"schema_version":"1.0","source":{"id":"1207.5902","kind":"arxiv","version":1}},"canonical_sha256":"d749d5c060fb89a4b9ac96135dbc7a257a361b221d36a73be4112e8f9bbf9e79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d749d5c060fb89a4b9ac96135dbc7a257a361b221d36a73be4112e8f9bbf9e79","first_computed_at":"2026-05-18T03:50:09.974033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:09.974033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"05fnA/8XuTcE2nskJLQlUtvdJH4Or2ldztRfAzCuMbnOpsp6xDA8X2RcLjV9ijbMLO5lkP1heubytXebUCFYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:09.974784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3451ebdae0bcf6a45e02c06cd30b5b3f7fc121cc297bf76676a014ca2be80ea7","sha256:8c8a0337fcd76b812f6970ef37ed44e8c1b62f02df7eba293cd3f8465210c529"],"state_sha256":"6592d190a9851f3e6a9c9fba1e03a99dacdfa6757a51b8da4902c350b860c445"}