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Eigenstructure of the infinitely-many-neutral-alleles diffusion model

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

S. N. Ethier
S. N. Ethier*
Affiliation:
University of Utah
*
∗Postal address: Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA. Research supported in part by NSF grant DMS-8902991.
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Abstract

The complete set of eigenvalues is found for the (unlabeled) infinitely-many-neutral-alleles diffusion model. The transition density for the process, originally derived by Griffiths, is rederived as an eigenfunction expansion.

Keywords

POPULATION GENETICSINFINITE-DIMENSIONAL DIFFUSION PROCESSPOISSON-DIRICHLET DISTRIBUTIONEWENS' SAMPLING FORMULASYMMETRIC OPERATOREIGENFUNCTION EXPANSIONTRANSITION DENSITY

MSC classification

Primary: 60J35: Transition functions, generators and resolvents
Secondary: 92D15: Problems related to evolution
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 487 - 498
Copyright
Copyright © Applied Probability Trust 1992 

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References

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