Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22062
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.
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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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|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|
|Deposited On:||07 Apr 2010 12:45|
|Last Modified:||05 Apr 2016 13:25|
|Publisher:||Institute of Mathematical Statistics|
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