Electronic Journal of Probability
- Electron. J. Probab.
- Volume 15 (2010), paper no. 26, 776-800.
On the Two Oldest Families for the Wright-Fisher Process
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.
Electron. J. Probab., Volume 15 (2010), paper no. 26, 776-800.
Accepted: 4 June 2010
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
This work is licensed under aCreative Commons Attribution 3.0 License.
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