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Wandering phenomena in infinite-allelic diffusion models

Published online by Cambridge University Press:  01 July 2016

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

We introduce a class of infinite-dimensional diffusion processes which contains a limiting version of the Ohta–Kimura model in population genetics. For this a necessary and sufficient condition for existence of stationary distributions is obtained. We are especially interested in the case where there is no stationary distribution. Then it is shown that an individual ergodic theorem holds for a suitably centralized process. As a corollary the wandering distribution exists.

Keywords

WANDERING PHENOMENAWANDERING DISTRIBUTIONINFINITE-ALLELE MODELINFINITE-DIMENSIONAL DIFFUSION PROCESSESPOPULATION GENETICSOHTA–KIMURA MODELSTATIONARY DISTRIBUTIONEMPIRICAL MEAN PROCESSPROCESS OF CENTERED DISTRIBUTIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 3 , September 1982 , pp. 457 - 483
Copyright
Copyright © Applied Probability Trust 1982 

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