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A transition function expansion for a diffusion model with selection


Barbour, A D; Ethier, S; Griffiths, R (2000). A transition function expansion for a diffusion model with selection. Annals of Applied Probability, 10(1):123-162.

Abstract

Using duality, an expansion is found for the transition function of the reversible $K$-allele diffusion model in population genetics. In the neutral case, the expansion is explicit but already known. When selection is present, it depends on the distribution at time $t$ of a specified $K$-type birth-and-death process starting at "infinity". The latter process is constructed by means of a coupling argument and characterized as the Ray process corresponding to the Ray–Knight compactification of the $K$-dimensional nonnegative-integer lattice.

Using duality, an expansion is found for the transition function of the reversible $K$-allele diffusion model in population genetics. In the neutral case, the expansion is explicit but already known. When selection is present, it depends on the distribution at time $t$ of a specified $K$-type birth-and-death process starting at "infinity". The latter process is constructed by means of a coupling argument and characterized as the Ray process corresponding to the Ray–Knight compactification of the $K$-dimensional nonnegative-integer lattice.

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13 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Finite-dimensional diffusion process; population genetics; duality; reversibility; multitype birth-and-death process; coupling; Ray-Knight compactification
Language:English
Date:2000
Deposited On:07 Apr 2010 12:45
Last Modified:05 Apr 2016 13:25
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Publisher DOI:https://doi.org/10.1214/aoap/1019737667
Permanent URL: https://doi.org/10.5167/uzh-22062

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