Poisson-Dirichlet distribution with small mutation rate

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Feng, Shui

关键词: Poisson-Dirichlet distribution;    Dirichlet process;    Homozygosity;    Large deviations;    Selection;   

DOI  :  10.1016/j.spa.2008.11.002

来源: Elsevier

【 摘 要 】

A large deviation principle is established for the Poisson-Dirichlet distribution when the mutation rate theta converges to zero. The rate function is identified explicitly, and takes on finite values only on states that have finite number of alleles. This result is then applied to the study of the asymptotic behavior of the homozygosity, and the Poisson-Dirichlet distribution with selection. The latter shows that several alleles can coexist when selection intensity goes to infinity in a particular way as theta approaches zero. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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