{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6O5FGT4RQZVKV4UV7FENCVH54B","short_pith_number":"pith:6O5FGT4R","schema_version":"1.0","canonical_sha256":"f3ba534f91866aaaf295f948d154fde041b6ce6ea3974eb1caafb0454063259a","source":{"kind":"arxiv","id":"1907.11894","version":1},"attestation_state":"computed","paper":{"title":"Escape probabilities of compound renewal processes with drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Javier Villarroel, Juan A. Vega, Miquel Montero","submitted_at":"2019-07-27T11:10:45Z","abstract_excerpt":"We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only negative jumps arise we give a general solution for escape and survival probabilities under Erlang$(n)$ and hypo-exponential arrivals. These ideas are generalized to the class of arrival distributions having rational Laplace transforms. In a general situation with two-sided jumps we also identify important families of solvable cases. A parallelism with the \"scal"},"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":"1907.11894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-27T11:10:45Z","cross_cats_sorted":[],"title_canon_sha256":"a89eff5bf79e5a2f6838fabedbbb58fa7e0cc09f7bff785915f47a69f1fa5a31","abstract_canon_sha256":"99ff7bc1bdf3802848a47e7a835081da6600ba702fd9826355880645a6d22071"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:22.634437Z","signature_b64":"eLF+13yphWnMCENtGkRUcGZZE/H61G1EARrB4XjRUqYqm9hnJ5OOnzsA/gUTKmbZH0bTsHKcAOsXthMkRsW0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3ba534f91866aaaf295f948d154fde041b6ce6ea3974eb1caafb0454063259a","last_reissued_at":"2026-05-17T23:39:22.633653Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:22.633653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Escape probabilities of compound renewal processes with drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Javier Villarroel, Juan A. Vega, Miquel Montero","submitted_at":"2019-07-27T11:10:45Z","abstract_excerpt":"We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only negative jumps arise we give a general solution for escape and survival probabilities under Erlang$(n)$ and hypo-exponential arrivals. These ideas are generalized to the class of arrival distributions having rational Laplace transforms. In a general situation with two-sided jumps we also identify important families of solvable cases. A parallelism with the \"scal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11894","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":"1907.11894","created_at":"2026-05-17T23:39:22.633777+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.11894v1","created_at":"2026-05-17T23:39:22.633777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11894","created_at":"2026-05-17T23:39:22.633777+00:00"},{"alias_kind":"pith_short_12","alias_value":"6O5FGT4RQZVK","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"6O5FGT4RQZVKV4UV","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"6O5FGT4R","created_at":"2026-05-18T12:33:10.108867+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/6O5FGT4RQZVKV4UV7FENCVH54B","json":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B.json","graph_json":"https://pith.science/api/pith-number/6O5FGT4RQZVKV4UV7FENCVH54B/graph.json","events_json":"https://pith.science/api/pith-number/6O5FGT4RQZVKV4UV7FENCVH54B/events.json","paper":"https://pith.science/paper/6O5FGT4R"},"agent_actions":{"view_html":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B","download_json":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B.json","view_paper":"https://pith.science/paper/6O5FGT4R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.11894&json=true","fetch_graph":"https://pith.science/api/pith-number/6O5FGT4RQZVKV4UV7FENCVH54B/graph.json","fetch_events":"https://pith.science/api/pith-number/6O5FGT4RQZVKV4UV7FENCVH54B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B/action/storage_attestation","attest_author":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B/action/author_attestation","sign_citation":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B/action/citation_signature","submit_replication":"https://pith.science/pith/6O5FGT4RQZVKV4UV7FENCVH54B/action/replication_record"}},"created_at":"2026-05-17T23:39:22.633777+00:00","updated_at":"2026-05-17T23:39:22.633777+00:00"}