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Total length of the genealogical tree for quadratic stationary continuous-state branching processes

Abstract : We prove the existence of the total length process for the genealogical tree of a population model with random size given by a quadratic stationary continuous-state branching processes. We also give, for the one-dimensional marginal, its Laplace transform as well as the fluctuation of the corresponding convergence. This result is to be compared with the one obtained by Pfaffelhuber and Wakolbinger for constant size population associated to the Kingman coalescent. We also give a time reversal property of the number of ancestors process at all time, and give a description of the so-called lineage tree in this model.
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https://hal.archives-ouvertes.fr/hal-01024986
Contributor : Hongwei Bi <>
Submitted on : Thursday, July 17, 2014 - 3:23:01 AM
Last modification on : Wednesday, July 27, 2016 - 2:48:48 PM

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Hongwei Bi, Jean-François Delmas. Total length of the genealogical tree for quadratic stationary continuous-state branching processes. 2014. ⟨hal-01024986⟩

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