{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D6U5Z26DKIS7TQMDIOQFRYZHTA","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":"a378a69971a5e139ebf117ada706638d52bea396f0a43571d43caa09e58124de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T09:32:03Z","title_canon_sha256":"fb4eda76e10e8d9459685e7b4f5cd1e57ca7115b5150b4d1113ab926b71c0fe8"},"schema_version":"1.0","source":{"id":"1306.2000","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2000","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2000v1","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2000","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"D6U5Z26DKIS7","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D6U5Z26DKIS7TQMD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D6U5Z26D","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:66a81baf9fb34f45afaf4a9be30986cb7977d8049c39a705bcc959bfbb0bd6a7","target":"graph","created_at":"2026-05-18T02:41:01Z","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":"Let $X_H(t), t\\ge 0$ be a fractional Brownian motion with Hurst index $H\\in(0,1}$ and define a gamma-reflected process $W_\\Ga(t)=X_H(t)-ct-\\gammainf_{s\\in[0,t]}\\left(X_H(s)-cs \\right)$, $t\\ge0$ with $c>0,\\gamma \\in [0,1]$ two given constants. In this paper we establish the exact tail asymptotic behaviour of $\\sup_{t\\in [0,T]} W_\\gamma(t)$ for any $T\\in (0,\\IF]$. Furthermore, we derive the exact tail asymptotic behaviour of the supremum of certain non-homogeneous mean-zero Gaussian random fields.","authors_text":"Enkelejd Hashorva, Lanpeng Ji, Vladimir I. Piterbarg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T09:32:03Z","title":"On the Supremum of gamma-reflected Processes with Fractional Brownian Motion as Input"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2000","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":"sha256:07560af290d8a0f2cd7af1186fd62c4ae4dfc6ecb7cdc933ee9fab9089433d26","target":"record","created_at":"2026-05-18T02:41:01Z","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":"a378a69971a5e139ebf117ada706638d52bea396f0a43571d43caa09e58124de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T09:32:03Z","title_canon_sha256":"fb4eda76e10e8d9459685e7b4f5cd1e57ca7115b5150b4d1113ab926b71c0fe8"},"schema_version":"1.0","source":{"id":"1306.2000","kind":"arxiv","version":1}},"canonical_sha256":"1fa9dcebc35225f9c18343a058e327983c876d625ea3e11040ad7ca5d93a7fac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fa9dcebc35225f9c18343a058e327983c876d625ea3e11040ad7ca5d93a7fac","first_computed_at":"2026-05-18T02:41:01.263390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:01.263390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F7oH7w4HgPHlAhJaAZV2dBv07EA5rSUfwgRs21oXVPe9AKmF48ZpPLrKR/TeLju9DiD+brBj4bx9H9HgzaQyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:01.263885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2000","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07560af290d8a0f2cd7af1186fd62c4ae4dfc6ecb7cdc933ee9fab9089433d26","sha256:66a81baf9fb34f45afaf4a9be30986cb7977d8049c39a705bcc959bfbb0bd6a7"],"state_sha256":"806f40c91ffb2e64df0296bb98f20b65a089210385a87741bcfdb8a77553b2de"}