{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VBNDA4WWFXFADTPLEKPS5P6MGP","short_pith_number":"pith:VBNDA4WW","schema_version":"1.0","canonical_sha256":"a85a3072d62dca01cdeb229f2ebfcc33c0781bf8d0dddf661ee455e007782067","source":{"kind":"arxiv","id":"1101.1034","version":1},"attestation_state":"computed","paper":{"title":"On the Ruin Probability of the Generalised Ornstein-Uhlenbeck Process in the Cram\\'er Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Claudia Kl\\\"uppelberg, Damien Bankowski, Ross Maller","submitted_at":"2011-01-05T17:20:52Z","abstract_excerpt":"For a bivariate \\Levy process $(\\xi_t,\\eta_t)_{t\\ge 0}$ and initial value $V_0$ define the Generalised Ornstein-Uhlenbeck (GOU) process \\[ V_t:=e^{\\xi_t}\\Big(V_0+\\int_0^t e^{-\\xi_{s-}}\\ud \\eta_s\\Big),\\quad t\\ge0,\\] and the associated stochastic integral process \\[Z_t:=\\int_0^t e^{-\\xi_{s-}}\\ud \\eta_s,\\quad t\\ge0.\\] Let $T_z:=\\inf\\{t>0:V_t<0\\mid V_0=z\\}$ and $\\psi(z):=P(T_z<\\infty)$ for $z\\ge 0$ be the ruin time and infinite horizon ruin probability of the GOU. Our results extend previous work of Nyrhinen (2001) and others to give asymptotic estimates for $\\psi(z)$ and the distribution of $T_z$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.1034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-05T17:20:52Z","cross_cats_sorted":[],"title_canon_sha256":"6e07af5ba990c884fad1c60e32f8ea54bd9a88a1a72984f3af9c8dbbff0f3711","abstract_canon_sha256":"0c748cd08160e20bd24aac024c0a7e9eb11d99de348359cc5d1ad466677839ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:01.004543Z","signature_b64":"5kM4z/2S+zjjBGCAWp19ZcRWowKPgeams2ab0I4H7BkMj50/GzqFfOHyPfijPiPUSsCp7WjWj/ye9kVrpYSSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a85a3072d62dca01cdeb229f2ebfcc33c0781bf8d0dddf661ee455e007782067","last_reissued_at":"2026-05-18T04:32:01.003969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:01.003969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Ruin Probability of the Generalised Ornstein-Uhlenbeck Process in the Cram\\'er Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Claudia Kl\\\"uppelberg, Damien Bankowski, Ross Maller","submitted_at":"2011-01-05T17:20:52Z","abstract_excerpt":"For a bivariate \\Levy process $(\\xi_t,\\eta_t)_{t\\ge 0}$ and initial value $V_0$ define the Generalised Ornstein-Uhlenbeck (GOU) process \\[ V_t:=e^{\\xi_t}\\Big(V_0+\\int_0^t e^{-\\xi_{s-}}\\ud \\eta_s\\Big),\\quad t\\ge0,\\] and the associated stochastic integral process \\[Z_t:=\\int_0^t e^{-\\xi_{s-}}\\ud \\eta_s,\\quad t\\ge0.\\] Let $T_z:=\\inf\\{t>0:V_t<0\\mid V_0=z\\}$ and $\\psi(z):=P(T_z<\\infty)$ for $z\\ge 0$ be the ruin time and infinite horizon ruin probability of the GOU. Our results extend previous work of Nyrhinen (2001) and others to give asymptotic estimates for $\\psi(z)$ and the distribution of $T_z$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1034","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.1034","created_at":"2026-05-18T04:32:01.004068+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1034v1","created_at":"2026-05-18T04:32:01.004068+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1034","created_at":"2026-05-18T04:32:01.004068+00:00"},{"alias_kind":"pith_short_12","alias_value":"VBNDA4WWFXFA","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"VBNDA4WWFXFADTPL","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"VBNDA4WW","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP","json":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP.json","graph_json":"https://pith.science/api/pith-number/VBNDA4WWFXFADTPLEKPS5P6MGP/graph.json","events_json":"https://pith.science/api/pith-number/VBNDA4WWFXFADTPLEKPS5P6MGP/events.json","paper":"https://pith.science/paper/VBNDA4WW"},"agent_actions":{"view_html":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP","download_json":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP.json","view_paper":"https://pith.science/paper/VBNDA4WW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1034&json=true","fetch_graph":"https://pith.science/api/pith-number/VBNDA4WWFXFADTPLEKPS5P6MGP/graph.json","fetch_events":"https://pith.science/api/pith-number/VBNDA4WWFXFADTPLEKPS5P6MGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP/action/storage_attestation","attest_author":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP/action/author_attestation","sign_citation":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP/action/citation_signature","submit_replication":"https://pith.science/pith/VBNDA4WWFXFADTPLEKPS5P6MGP/action/replication_record"}},"created_at":"2026-05-18T04:32:01.004068+00:00","updated_at":"2026-05-18T04:32:01.004068+00:00"}