MODERATE DEVIATIONS FOR POISSON-DIRICHLET DISTRIBUTION

• 成果类型: Article
• 署名作者: Feng, Shui; Ga, Fuqing
• 署名单位: McMaster University; Wuhan University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP501
• 发表日期: 2008
• 页码: 1794-1824
• 关键词: ewens sampling formula; independent increments; random-variables; diffusion-model; stationary; selection; Mutation; LIMITS

摘要

The Poisson-Dirichlet distribution arises in many different areas. The parameter theta in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of theta approaching infinity is practically motivated and has led to new, interesting mathematical structures. Laws of large numbers, fluctuation theorems and large-deviation results have been established. In this paper, moderate-deviation principles are established for the Poisson-Dirichlet distribution, the GEM distribution, the homozygosity, and the Dirichlet process when the parameter theta approaches infinity. These results, combined with earlier work, not only provide a relatively complete picture of the asymptotic behavior of the Poisson-Dirichlet distribution for large theta, but also lead to a better understanding of the large deviation problem associated with the scaled homozygosity. They also reveal some new structures that are not observed in existing large-deviation results.