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Poisson-Dirichlet distribution with small mutation rate

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  • Feng, Shui

Abstract

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.

Suggested Citation

  • Feng, Shui, 2009. "Poisson-Dirichlet distribution with small mutation rate," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2082-2094, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:2082-2094
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    References listed on IDEAS

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    1. Ethier, S. N. & Kurtz, Thomas G., 1994. "Convergence to Fleming-Viot processes in the weak atomic topology," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 1-27, November.
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    Cited by:

    1. Zhou, Youzhou, 2014. "Asymptotic behaviour of an infinitely-many-alleles diffusion with symmetric overdominance," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2771-2798.
    2. Feng, Shui & Gao, Fuqing, 2010. "Asymptotic results for the two-parameter Poisson-Dirichlet distribution," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1159-1177, July.

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