{"paper":{"title":"A Delayed Yule Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Edward C. Waymire, Enrique Thomann, Nicholas Michalowski, Radu Dascaliuc","submitted_at":"2016-07-07T17:26:30Z","abstract_excerpt":"In now classic work, David Kendall (1966) recognized that the Yule process and Poisson process could be related by a (random) time change. Furthermore, he showed that the Yule population size rescaled by its mean has an almost sure exponentially distributed limit as $t\\to \\infty$. In this note we introduce a class of coupled delayed Yule processes parameterized by $0 < \\alpha \\le 1$ that includes the Poisson process at $\\alpha = {1/2}$. Moreover we extend Kendall's limit theorem to include a larger class of positive martingales derived from functionals that gauge the population genealogy. A so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02092","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"}