{"paper":{"title":"Convergence of a Critical Multitype Bellman--Harris Process with Finite-Mean Lifetimes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E.T. Kolkovska, J.A. L\\'opez-Mimbela, J.H. Ram\\'irez-Gonz\\'alez","submitted_at":"2024-10-22T19:09:14Z","abstract_excerpt":"We study a critical multitype Bellman--Harris branching particle system in \\(\\mathbb R^N\\) with a finite type space \\(\\mathbf K=\\{1,\\dots,K\\}\\). Particles of type \\(I\\) move according to a symmetric \\(\\alpha_i\\)-stable process, have non-arithmetic lifetimes with finite mean, and reproduce according to a critical offspring law whose mean matrix is irreducible and stochastic. The branching mechanism is assumed to be in the domain of attraction of a \\((1+\\beta)\\)-stable law, with \\(\\beta\\in(0,1]\\). We prove that the particle system converges, as \\(t\\to\\infty\\), to a limiting random measure which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17369","kind":"arxiv","version":2},"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/2410.17369/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"}