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Ergodic Inequality of a Two-Parameter Infinitely-Many-Alleles Diffusion Model

Part of: Ergodic theory Markov processes

Published online by Cambridge University Press:  30 January 2018

Youzhou Zhou
Youzhou Zhou*
Affiliation:
McMaster University
*
∗ Postal address: School of Statistics and Mathematics, Zhongnan University of Economics and Law, 182 South Lake Avenue, East Lake New Technology Development Zone, Wuhan, Hubei, China 430073. Email address: youzhouzhou1984@gmail.com
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Abstract

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In this paper three models are considered. They are the infinitely-many-neutral-alleles model of Ethier and Kurtz (1981), the two-parameter infinitely-many-alleles diffusion model of Petrov (2009), and the infinitely-many-alleles model with symmetric dominance Ethier and Kurtz (1998). New representations of the transition densities are obtained for the first two models and the ergodic inequalities are provided for all three models.

Keywords

Two-parameter Poisson-Dirichlet distributiontransition densityergodic inequality

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 238 - 246
Copyright
© Applied Probability Trust 

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