{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TVUFJG57KUNEZRU2L263YW5C5P","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":"5e49371dce3de675cfd450e1f0488f5d2ada9076393ab5bd55a3b9dd3b431d62","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2020-11-25T21:24:19Z","title_canon_sha256":"2564d31821f53873c32f00cc48515c08d5cf1ebf6f73f11f9457c6343b70534d"},"schema_version":"1.0","source":{"id":"2011.13030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.13030","created_at":"2026-07-05T01:54:50Z"},{"alias_kind":"arxiv_version","alias_value":"2011.13030v1","created_at":"2026-07-05T01:54:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.13030","created_at":"2026-07-05T01:54:50Z"},{"alias_kind":"pith_short_12","alias_value":"TVUFJG57KUNE","created_at":"2026-07-05T01:54:50Z"},{"alias_kind":"pith_short_16","alias_value":"TVUFJG57KUNEZRU2","created_at":"2026-07-05T01:54:50Z"},{"alias_kind":"pith_short_8","alias_value":"TVUFJG57","created_at":"2026-07-05T01:54:50Z"}],"graph_snapshots":[{"event_id":"sha256:d02d82e227894af34767f030efb000c96b62c4f38760a403cd2d7b5fffe2dc45","target":"graph","created_at":"2026-07-05T01:54:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.13030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated volatility process arising in general mild solutions of Hilbert space-valued stochastic evolution equations in the sense of Da Prato and Zabczyk (2014). We prove a weak law of large numbers for this estimator, where the convergence is uniform on compacts in probability with respect to the Hilbert-Schmidt norm. In addition, we show that the conditions on the vola","authors_text":"Almut E. D. Veraart, Dennis Schroers, Fred Espen Benth","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2020-11-25T21:24:19Z","title":"A weak law of large numbers for realised covariation in a Hilbert space setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.13030","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:d91261f83278f8eebb590995d9ebcaf256ad6f907c0de7a956f4cff0752a4e52","target":"record","created_at":"2026-07-05T01:54:50Z","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":"5e49371dce3de675cfd450e1f0488f5d2ada9076393ab5bd55a3b9dd3b431d62","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2020-11-25T21:24:19Z","title_canon_sha256":"2564d31821f53873c32f00cc48515c08d5cf1ebf6f73f11f9457c6343b70534d"},"schema_version":"1.0","source":{"id":"2011.13030","kind":"arxiv","version":1}},"canonical_sha256":"9d68549bbf551a4cc69a5ebdbc5ba2ebf348bebb4852bf811cf7a86cba560794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d68549bbf551a4cc69a5ebdbc5ba2ebf348bebb4852bf811cf7a86cba560794","first_computed_at":"2026-07-05T01:54:50.073657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:54:50.073657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TrIi7Bxmp5co/MIfs00RzU/+FU230IIO1mX7rYtmZ4OU8pLsS8AQp3eOPbfGAk5OWsQvkm5HvrMuQ+W5jaZ1Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:54:50.074089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.13030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d91261f83278f8eebb590995d9ebcaf256ad6f907c0de7a956f4cff0752a4e52","sha256:d02d82e227894af34767f030efb000c96b62c4f38760a403cd2d7b5fffe2dc45"],"state_sha256":"57c480d5fa090ced22e09b2703283133c3ba760e626f241a1801f560eef2e000"}