{"paper":{"title":"Approximation of birth-death processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Liping Li","submitted_at":"2024-09-08T08:16:27Z","abstract_excerpt":"The birth-death process is a special type of continuous-time Markov chain with index set $\\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\\gamma, \\beta, \\nu)$, where $\\gamma$ and $\\beta$ are non-negative constants, and $\\nu$ is a positive measure on $\\mathbb{N}$. By employing the Ray-Knight compactification, the birth-death process can be realized as a c\\`adl\\`ag process with strong Markov property on the one-point compactification space $\\overline{\\mathbb{N}}_{\\partial}$, which includes an additional cemetery point $\\partial$. In a certain sense, the thre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.05018","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/2409.05018/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"}