{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:M3TAM5EGTONJPU4LZXPY766REM","short_pith_number":"pith:M3TAM5EG","schema_version":"1.0","canonical_sha256":"66e60674869b9a97d38bcddf8ffbd1232e5ca1d28602d8fa29e44825478f7028","source":{"kind":"arxiv","id":"1902.01162","version":1},"attestation_state":"computed","paper":{"title":"Boundary behavior of multi-type continuous-state branching processes with immigration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Barbara R\\\"udiger, Martin Friesen, Peng Jin","submitted_at":"2019-02-04T13:15:45Z","abstract_excerpt":"In this article we provide a sufficient condition for a continuous-state branching process with immigration (CBI process) to not hit its boundary, i.e. for non-extinction. Our result applies to arbitrary dimension $d \\geq 1$ and is formulated in terms of an integrability condition for its immigration and branching mechanisms $F$ and $R$. The proof is based on a suitable comparison with one-dimensional CBI processes and an existing result for one-dimensional CBI processes. The same technique is also used to provide a sufficient condition for transience of multi-type CBI processes."},"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":"1902.01162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-04T13:15:45Z","cross_cats_sorted":[],"title_canon_sha256":"c1eb75c9ae2cf241b4cac5f950de3cffacb25d38d0c0d78523fa725e0dc496ad","abstract_canon_sha256":"38057a751b788ebf335f6fe691450aab9cb9c1def47f22c9e744b09e74f16fc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:05:27.707292Z","signature_b64":"nlCBbIGeQXEQeoU7aYEJQ0UVOlTa2fjDQe7i0CKVfXn49PYz88KyotIQR1DJN6Qnl7wRZ4D7//WFIY1Jk/2jCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66e60674869b9a97d38bcddf8ffbd1232e5ca1d28602d8fa29e44825478f7028","last_reissued_at":"2026-07-05T04:05:27.706646Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:05:27.706646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary behavior of multi-type continuous-state branching processes with immigration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Barbara R\\\"udiger, Martin Friesen, Peng Jin","submitted_at":"2019-02-04T13:15:45Z","abstract_excerpt":"In this article we provide a sufficient condition for a continuous-state branching process with immigration (CBI process) to not hit its boundary, i.e. for non-extinction. Our result applies to arbitrary dimension $d \\geq 1$ and is formulated in terms of an integrability condition for its immigration and branching mechanisms $F$ and $R$. The proof is based on a suitable comparison with one-dimensional CBI processes and an existing result for one-dimensional CBI processes. The same technique is also used to provide a sufficient condition for transience of multi-type CBI processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01162","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.01162/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1902.01162","created_at":"2026-07-05T04:05:27.706727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.01162v1","created_at":"2026-07-05T04:05:27.706727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01162","created_at":"2026-07-05T04:05:27.706727+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3TAM5EGTONJ","created_at":"2026-07-05T04:05:27.706727+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3TAM5EGTONJPU4L","created_at":"2026-07-05T04:05:27.706727+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3TAM5EG","created_at":"2026-07-05T04:05:27.706727+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.05473","citing_title":"On the anisotropic stable JCIR process","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM","json":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM.json","graph_json":"https://pith.science/api/pith-number/M3TAM5EGTONJPU4LZXPY766REM/graph.json","events_json":"https://pith.science/api/pith-number/M3TAM5EGTONJPU4LZXPY766REM/events.json","paper":"https://pith.science/paper/M3TAM5EG"},"agent_actions":{"view_html":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM","download_json":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM.json","view_paper":"https://pith.science/paper/M3TAM5EG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.01162&json=true","fetch_graph":"https://pith.science/api/pith-number/M3TAM5EGTONJPU4LZXPY766REM/graph.json","fetch_events":"https://pith.science/api/pith-number/M3TAM5EGTONJPU4LZXPY766REM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM/action/storage_attestation","attest_author":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM/action/author_attestation","sign_citation":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM/action/citation_signature","submit_replication":"https://pith.science/pith/M3TAM5EGTONJPU4LZXPY766REM/action/replication_record"}},"created_at":"2026-07-05T04:05:27.706727+00:00","updated_at":"2026-07-05T04:05:27.706727+00:00"}