Particle representations for measure-valued population models

• 成果类型: Article
• 署名作者: Donnelly, P; Kurtz, TG
• 署名单位: University of Oxford; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1999
• 页码: 166-205
• 关键词: branching diffusions; superprocesses; extinction; INTEGRALS; EQUATIONS

摘要

Models of populations in which a type or location, represented by a point in a metric space E, is associated with each individual in the population are considered. A population process is neutral if the chances of an individual replicating or dying do not depend on its type. Measure-valued processes are obtained as infinite population limits for a large class of neutral population models, and it is shown that these measure-valued processes can be represented in terms of the total mass of the population and the de Finetti measures associated with an E-alpha-valued particle model X = (X-1, X-2,...) such that, for each t greater than or equal to 0, (X-1(t), X-2(t),...) is exchangeable. The construction gives an explicit connection between genealogical and diffusion models in population genetics. The class of measure-valued models covered includes both neutral Fleming-Viot and Dawson-Watanabe processes. The particle model gives a simple representation of the Dawson-Perkins historical process and Perkins's historical stochastic integral can be obtained in terms of classical semimartingale integration. A number of applications bo new and known results on conditioning, uniqueness and limiting behavior are described.