{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5ZQB56PAYUM54O4EV5VUXFVPX6","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":"86d2b6f0462ec03191169624a9bfda602b15b1f2d66fd51d1b9325907a1289df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T16:18:05Z","title_canon_sha256":"ee9252af1c821db8047755f33877e2320aead72aff285b72a71541560d898122"},"schema_version":"1.0","source":{"id":"1711.03448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03448","created_at":"2026-05-18T00:30:56Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03448v1","created_at":"2026-05-18T00:30:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03448","created_at":"2026-05-18T00:30:56Z"},{"alias_kind":"pith_short_12","alias_value":"5ZQB56PAYUM5","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5ZQB56PAYUM54O4E","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5ZQB56PA","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:dd1572c1e2bc18670305f923e667f26caf75f80892a32b88ea90bda031181920","target":"graph","created_at":"2026-05-18T00:30:56Z","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":"In this paper, we consider stationarity of a class of second-order stochastic evolution equations with memory, driven by Wiener processes or Levy jump processes, in Hilbert spaces. The strategy is to formulate by reduction some first-order systems in connection with the stochastic equations under investigation. We develop asymptotic behavior of dissipative second-order equations and then apply them to time delay systems through Gearhart-Pruss-Greiner's theorem. The stationary distribution of the system under consideration is the projection on the first coordinate of the corresponding stationar","authors_text":"Kai Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T16:18:05Z","title":"Stationary Distributions of Second Order Stochastic Evolution Equations with Memory in Hilbert Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03448","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:a9900a6746546da4348a01b3151dae42536557dc915c1376c75c62c47da5d2c1","target":"record","created_at":"2026-05-18T00:30:56Z","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":"86d2b6f0462ec03191169624a9bfda602b15b1f2d66fd51d1b9325907a1289df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T16:18:05Z","title_canon_sha256":"ee9252af1c821db8047755f33877e2320aead72aff285b72a71541560d898122"},"schema_version":"1.0","source":{"id":"1711.03448","kind":"arxiv","version":1}},"canonical_sha256":"ee601ef9e0c519de3b84af6b4b96afbf8ab87a250ebb53be408344c8d670780a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee601ef9e0c519de3b84af6b4b96afbf8ab87a250ebb53be408344c8d670780a","first_computed_at":"2026-05-18T00:30:56.056783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:56.056783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DRechLMKZ/oqohFLt2dk96PG8MBME2y0EbE63WwCj3/4UFbkspfOIDFH+0TFBPsrVZVuo2SH3Se+jG0yYyUMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:56.057508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9900a6746546da4348a01b3151dae42536557dc915c1376c75c62c47da5d2c1","sha256:dd1572c1e2bc18670305f923e667f26caf75f80892a32b88ea90bda031181920"],"state_sha256":"1785be2532010801c96dc98a3e7b96c69d9e647761150e98236f16171249b73e"}