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Article Dans Une Revue Electronic Journal of Probability Année : 2010

On the two oldest families for the Wright-Fisher process

Résumé

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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Dates et versions

hal-00674632 , version 1 (27-02-2012)

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  • HAL Id : hal-00674632 , version 1

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Jean-François Delmas, Jean-Stephane Dhersin, Arno Siri-Jegousse. On the two oldest families for the Wright-Fisher process. Electronic Journal of Probability, 2010, 15, pp.776-800. ⟨hal-00674632⟩
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