WEAK-CONVERGENCE TO A MARKOV-CHAIN WITH AN ENTRANCE BOUNDARY - ANCESTRAL PROCESSES IN POPULATION-GENETICS

• 成果类型: Article
• 署名作者: DONNELLY, P
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990336
• 发表日期: 1991
• 页码: 1102-1117
• 关键词: model

摘要

We derive conditions under which a sequence of processes will converge to a (continuous-time) Markov chain with an entrance boundary. Our main application of this result is in proving weak convergence of the so-called population ancestral processes, associated with a wide class of exchangeable reproductive models, to a particular death process with an entrance boundary at infinity. This settles a conjecture of Kingman. We also prove weak convergence of the absorption times of many neutral genetics models to that of the Wright-Fisher diffusion, and convergence of population line-of-descent processes to another death process.