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February 2000 A transition function expansion for a diffusion model with selection
A. D. Barbour, S. N. Ethier, R. C. Griffiths
Ann. Appl. Probab. 10(1): 123-162 (February 2000). DOI: 10.1214/aoap/1019737667


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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A. D. Barbour. S. N. Ethier. R. C. Griffiths. "A transition function expansion for a diffusion model with selection." Ann. Appl. Probab. 10 (1) 123 - 162, February 2000.


Published: February 2000
First available in Project Euclid: 25 April 2002

zbMATH: 1171.60368
MathSciNet: MR1765206
Digital Object Identifier: 10.1214/aoap/1019737667

Primary: 60J27 , 60J35 , 60J60
Secondary: 92D10

Keywords: coupling , Duality , Finite-dimensional diffusion process , multitype birth-and-death process , Population genetics , Ray-Knight compactification , reversibility

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 1 • February 2000
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