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.
@article{1019737667,
author = {Barbour, A. D. and Ethier, S. N. and Griffiths, R. C.},
title = {A transition function expansion for a diffusion model with
selection},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 123-162},
language = {en},
url = {http://dml.mathdoc.fr/item/1019737667}
}
Barbour, A. D.; Ethier, S. N.; Griffiths, R. C. A transition function expansion for a diffusion model with
selection. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 123-162. http://gdmltest.u-ga.fr/item/1019737667/