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Limit diffusions of some stepping-stone models

Published online by Cambridge University Press:  14 July 2016

Ken-Iti Sato
Ken-Iti Sato*
Affiliation:
Kanazawa University
*
∗ Postal address: Department of Mathematics, College of Liberal Arts, Kanazawa University, Kanazawa, Japan.
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Abstract

A Markov chain model of a population consisting of a finite or countably infinite number of colonies with N particles at each colony is considered. There are d types of particle and transition from the nth generation to the (n + 1)th is made up of three stages: reproduction, migration, and sampling. Natural selection works in the reproduction stage. The limiting diffusion operator (as N→∞) for the proportion of types at colonies is found. Convergence to the diffusion is proved under certain conditions.

Keywords

MARKOV CHAINOFFSPRING DISTRIBUTIONSTEPPING-STONE STRUCTUREINFINITE-DIMENSIONAL DIFFUSIONMARTINGALE PROBLEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 460 - 471
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This work was done while the author was visiting Carleton University, supported by the Natural Science and Engineering Research Council Canada, the Japan Society for the Promotion of Science, and the NSERC operating grant of D. A. Dawson.

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