{"paper":{"title":"CLT for supercritical branching processes with heavy-tailed branching law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Piotr Mi{\\l}o\\'s, Rafa{\\l} Marks","submitted_at":"2018-03-14T19:47:01Z","abstract_excerpt":"Consider a branching system with particles moving according to an Ornstein-Uhlenbeck process with drift $\\mu>0$ and branching according to a law in the domain of attraction of the $(1+\\beta)$-stable distribution. The mean of the branching law is strictly larger than $1$ implying that the system is supercritical and the total number of particles grows exponentially at some rate $\\lambda>0$.\n  It is known that the system obeys a law of large numbers. In the paper we study its rate of convergence.\n  We discover an interesting interplay between the branching rate $\\lambda$ and the drift parameter "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05491","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":""},"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"}