Splitting trees with neutral Poissonian mutations I: Small families
AbstractWe consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate b. Such a genealogical tree is usually called a splitting tree , and the population counting process (Nt;t≥0) is a homogeneous, binary Crump–Mode–Jagers process.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 122 (2012)
Issue (Month): 3 ()
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- Geiger, Jochen, 1996. "Size-biased and conditioned random splitting trees," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 187-207, December.
- Bertoin, Jean, 2010. "A limit theorem for trees of alleles in branching processes with rare neutral mutations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 678-697, May.
- Champagnat, Nicolas & Lambert, Amaury, 2013. "Splitting trees with neutral Poissonian mutations II: Largest and oldest families," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1368-1414.
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