ASYMPTOTIC REGIMES FOR THE PARTITION INTO COLONIES OF A BRANCHING PROCESS WITH EMIGRATION

• 成果类型: Article
• 署名作者: Bertoin, Jean
• 署名单位: Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP678
• 发表日期: 2010
• 页码: 1967-1988
• 关键词: neutral mutations; alleles

摘要

We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are interested in asymptotics of the partition of the total population into colonies for large populations with rare migrations. Under appropriate regimes, we establish weak convergence of the rescaled partition to some random measure that is constructed from the restriction of a Poisson point measure to a certain random region, and whose cumulant solves a simple integral equation.