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.
https://hal-enpc.archives-ouvertes.fr/hal-00674632
Contributeur : Cermics Hal
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Soumis le : lundi 27 février 2012 - 17:21:03
Dernière modification le : jeudi 11 avril 2019 - 16:02:09
Jean-François Delmas, Jean-Stephane Dhersin, Arno Siri-Jegousse. On the two oldest families for the Wright-Fisher process. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010, 15, pp.776-800. ⟨hal-00674632⟩
