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.
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