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On convergence to diffusion processes of Markov chains related to population genetics

Published online by Cambridge University Press:  01 July 2016

Norio Okada
Norio Okada*
Affiliation:
Tokyo Institute of Technology
*
∗Postal address: Department of Applied Physics, Tokyo Institute of Technology, Oh-Okayama, Tokyo, Japan.
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Abstract

A Markov chain model related to population genetics and its convergence to a diffusion process on the multi-dimensional bounded domain are treated. We discuss the case where natural selection is random and the different selection effects over successive generations are independent. Our model is a multi-allelic version of the haploid model of Karlin and Levikson. The asymptotic properties of the limiting diffusion are stated.

Keywords

MARKOV CHAINPOPULATION GENETICSRANDOM NATURAL SELECTIONDIFFUSION APPROXIMATIONMARTINGALE PROBLEMFIXATION PROBABILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 4 , December 1979 , pp. 673 - 700
Copyright
Copyright © Applied Probability Trust 1979 

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