{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4BANJYEHUDWX6LINRXS3U7ZP3P","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":"e1ae6fa9a2d5c77a4609d09c9c9f6241d62688816003e4327137056392167bdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-14T16:03:45Z","title_canon_sha256":"09efe64ccbdad61b89af1d7bb718cc9c49400589279f9b29b2d0a05212d8543a"},"schema_version":"1.0","source":{"id":"1508.03555","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03555","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03555v2","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03555","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"pith_short_12","alias_value":"4BANJYEHUDWX","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4BANJYEHUDWX6LIN","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4BANJYEH","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:eab5faa3f8e62ded39f7a0d72f3332c8202842ccf23aa81db0eba5dfda386a6e","target":"graph","created_at":"2026-05-18T01:24:18Z","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":"For a strictly stationary sequence of nonnegative regularly varying random variables $(X_{n})$ we study functional weak convergence of partial maxima processes $M_{n}(t) = \\bigvee_{i=1}^{\\lfloor nt \\rfloor}X_{i},\\,t \\in [0,1]$ in the space $D[0,1]$ with the Skorohod $J_{1}$ topology. Under the strong mixing condition, we give sufficient conditions for such convergence when clustering of large values do not occur. We apply this result to stochastic volatility processes. Further we give conditions under which the regular variation property is a necessary condition for $J_{1}$ and $M_{1}$ functio","authors_text":"Danijel Krizmani\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-14T16:03:45Z","title":"Functional weak convergence of partial maxima processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03555","kind":"arxiv","version":2},"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:b55db22d721a2de35502543e6faefdc8fdf1fa4231bd122d4ac00a4b4cc2e758","target":"record","created_at":"2026-05-18T01:24:18Z","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":"e1ae6fa9a2d5c77a4609d09c9c9f6241d62688816003e4327137056392167bdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-14T16:03:45Z","title_canon_sha256":"09efe64ccbdad61b89af1d7bb718cc9c49400589279f9b29b2d0a05212d8543a"},"schema_version":"1.0","source":{"id":"1508.03555","kind":"arxiv","version":2}},"canonical_sha256":"e040d4e087a0ed7f2d0d8de5ba7f2fdbea9fc38088be084668b1b68cef342418","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e040d4e087a0ed7f2d0d8de5ba7f2fdbea9fc38088be084668b1b68cef342418","first_computed_at":"2026-05-18T01:24:18.521624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:18.521624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Rl9vucl5kkBwgfsAkZfk2PfYULBh+5ZYK+4fFtDcCfGueVgBNui/PWhoCWUqw6Hzg5p7YrjWXtor07vf05hCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:18.522060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03555","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b55db22d721a2de35502543e6faefdc8fdf1fa4231bd122d4ac00a4b4cc2e758","sha256:eab5faa3f8e62ded39f7a0d72f3332c8202842ccf23aa81db0eba5dfda386a6e"],"state_sha256":"3d36c07be529ae9022101d4008ca8e106a21f9fba134c1e8f32e05b84459a85a"}