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On the Two Oldest Families for the Wright-Fisher Process


 
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1. Title Title of document On the Two Oldest Families for the Wright-Fisher Process
 
2. Creator Author's name, affiliation, country Jean-François Delmas; École des Ponts and Université Paris-Est; France
 
2. Creator Author's name, affiliation, country Jean-Stéphane Dhersin; Université Paris 13; France
 
2. Creator Author's name, affiliation, country Arno Siri-Jegousse; Université Paris Descartes; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Wright-Fisher diffusion, MRCA, Kingman coalescent tree, resurrected process, quasi-stationary distribution
 
3. Subject Subject classification 60J70, 60K35, 92D25
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) This work is partially supported by the ``Agence Nationale de la Recherche'', ANR-BLAN06-3-146282 and ANR-08-BLAN-0190.
 
7. Date (YYYY-MM-DD) 2010-06-04
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/771
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-771
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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