Electronic Journal of Probability

On the Two Oldest Families for the Wright-Fisher Process

Jean-François Delmas, Jean-Stéphane Dhersin, and Arno Siri-Jegousse

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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.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 26, 776-800.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819811

Digital Object Identifier
doi:10.1214/EJP.v15-771

Mathematical Reviews number (MathSciNet)
MR2653183

Zentralblatt MATH identifier
1226.60114

Subjects
Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 92D25: Population dynamics (general)

Keywords
Wright-Fisher diffusion MRCA Kingman coalescent tree resurrected process quasi-stationary distribution

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Delmas, Jean-François; Dhersin, Jean-Stéphane; Siri-Jegousse, Arno. On the Two Oldest Families for the Wright-Fisher Process. Electron. J. Probab. 15 (2010), paper no. 26, 776--800. doi:10.1214/EJP.v15-771. https://projecteuclid.org/euclid.ejp/1464819811


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