A SMALL-TIME COUPLING BETWEEN Λ-COALESCENTS AND BRANCHING PROCESSES

• 成果类型: Article
• 署名作者: Berestycki, Julien; Berestycki, Nathanael; Limic, Vlada
• 署名单位: Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP911
• 发表日期: 2014
• 页码: 449-475
• 关键词: stochastic flows; BEHAVIOR; limit

摘要

We describe a new general connection between Lambda-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the lookdown process of Donnelly and Kurtz. This coupling has the property that the coalescent comes down from infinity if and only if the branching process becomes extinct, thereby answering a question of Bertoin and Le Gall. The coupling also offers new perspective on the speed of coming down from infinity and allows us to relate power-law behavior for N-Lambda(t) to the classical upper and lower indices arising in the study of pathwise properties of Levy processes.