The coalescent point process of multi-type branching trees

Lea Popovic and Mariolys Rivas

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 4120-4148

Abstract: We define a multi-type coalescent point process of a general branching process with countably many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population providing types along ancestral lineages of all individuals in the standing population. We show that the coalescent process is a functional of a certain Markov chain defined by the planar embedding of the multi-type branching process.

Keywords: Genealogical tree; Coalescent point process; Multi-type branching process; Linear fractional distribution; Quasi-stationary distribution; Tree shape (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spa.2014.07.018

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