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2010 On the Two Oldest Families for the Wright-Fisher Process
Jean-François Delmas, Jean-Stéphane Dhersin, Arno Siri-Jegousse
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Electron. J. Probab. 15: 776-800 (2010). DOI: 10.1214/EJP.v15-771

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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Jean-François Delmas. Jean-Stéphane Dhersin. Arno Siri-Jegousse. "On the Two Oldest Families for the Wright-Fisher Process." Electron. J. Probab. 15 776 - 800, 2010. https://doi.org/10.1214/EJP.v15-771

Information

Accepted: 4 June 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60114
MathSciNet: MR2653183
Digital Object Identifier: 10.1214/EJP.v15-771

Subjects:
Primary: 60J70
Secondary: 60K35, 92D25

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