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Asymptotic behaviour of an infinitely-many-alleles diffusion with symmetric overdominance

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  • Zhou, Youzhou

Abstract

This paper considers the limiting distribution of πλ,θ, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance (Ethier and Kurtz, 1998). In Feng (2009) the large deviation principle for πλ,θ indicates that there are countably many phase transitions for the limiting distribution of πλ,θ, and the critical points are λ=k(k+1),k≥1. The asymptotic behaviours at those critical points, however, are unclear. This article provides a definite description of the critical cases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2771-2798
    DOI: 10.1016/j.spa.2014.03.011
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    References listed on IDEAS

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    1. Feng, Shui, 2009. "Poisson-Dirichlet distribution with small mutation rate," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2082-2094, June.
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