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 Electronic Journal of Probability > Vol. 15(2010) > Paper 26 open journal systems 


On the two oldest families for the Wright-Fisher process

Jean-François Delmas, Univ. Paris-Est, Cermics
Jean-Stéphane Dhersin, Univ. Paris 13
Arno Siri-Jegousse, MAP5, Univ. Paris Descartes


Abstract
We extend some of the results of Pfaffelhuber and Wakolbinger on the process of the most recent common ancestors in evolving coalescent by taking into account the size of one of the two oldest families or the oldest family which contains the immortal line of descent. For example we give an explicit formula for the Laplace transform of the extinction time for the Wright-Fisher diffusion. We give also an interpretation of the quasi-stationary distribution of the Wright-Fisher diffusion using the process of the relative size of one of the two oldest families, which can be seen as a resurrected Wright-Fisher diffusion.


Full text: PDF

Pages: 776-800

Published on: June 4, 2010
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Electronic Journal of Probability. ISSN: 1083-6489