{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EPJS5BD5UJMFCVYJAFKI3PU6AD","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":"df04a9fba20563af1428a43fb88a4088dddea9b2828ab6cee9a75d11d6425f58","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-01T14:32:21Z","title_canon_sha256":"372e75a78d16e577324e0e5e1fb692241bfc483c46a728d1a7f14a7d9a895f5e"},"schema_version":"1.0","source":{"id":"1205.0172","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0172","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0172v3","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0172","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"EPJS5BD5UJMF","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EPJS5BD5UJMFCVYJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EPJS5BD5","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:6f507a8de783a8fece4c53e89561e140e3546f577bf6a36659103160c6a74b66","target":"graph","created_at":"2026-05-18T02:20:20Z","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 article, we address the absorption properties of a class of stochastic differ- ential equations around singular points where both the drift and diffusion functions vanish. According to the H\\\"older coefficient alpha of the diffusion function around the singular point, we identify different regimes. Stability of the absorbing state, large deviations for the absorption time, existence of stationary or quasi-stationary distributions are discussed. In particular, we show that quasi-stationary distributions only exist for alpha < 3/4, and for alpha in the interval (3/4, 1), no quasi-station","authors_text":"Gilles Wainrib, Jonathan Touboul","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-01T14:32:21Z","title":"Absorption properties of stochastic equations with H\\\"older diffusion coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0172","kind":"arxiv","version":3},"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":"sha256:2f955a669541e3c264a88fb3f4be860e677a2e492844dc068841f95f1809d7c3","target":"record","created_at":"2026-05-18T02:20:20Z","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":"df04a9fba20563af1428a43fb88a4088dddea9b2828ab6cee9a75d11d6425f58","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-01T14:32:21Z","title_canon_sha256":"372e75a78d16e577324e0e5e1fb692241bfc483c46a728d1a7f14a7d9a895f5e"},"schema_version":"1.0","source":{"id":"1205.0172","kind":"arxiv","version":3}},"canonical_sha256":"23d32e847da25851570901548dbe9e00c856b4276bdf1f5e838ad05c59e9178d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23d32e847da25851570901548dbe9e00c856b4276bdf1f5e838ad05c59e9178d","first_computed_at":"2026-05-18T02:20:20.211911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:20.211911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6vrNoZXcoWHhcFOmkUzp8j502IFIh8Nax9of6LsOJK2BjxSZRNld9rK3GLe/SgJT/ltz98g5KFq+Z0ruUw7HBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:20.212546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0172","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f955a669541e3c264a88fb3f4be860e677a2e492844dc068841f95f1809d7c3","sha256:6f507a8de783a8fece4c53e89561e140e3546f577bf6a36659103160c6a74b66"],"state_sha256":"c1178c4189e55f6f3632194b1379c132a601274af68f6ff2291439b7af4dbd31"}