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November 2019 Uniform sampling in a structured branching population
Aline Marguet
Bernoulli 25(4A): 2649-2695 (November 2019). DOI: 10.3150/18-BEJ1066


We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event occurs, the trait of the descendants at birth depends on the trait of the mother and on the number of descendants. In this article, we explicitly describe the penalized Markov process, named auxiliary process, corresponding to the dynamic of the trait of a “typical” individual by giving its associated infinitesimal generator. We prove a Many-to-One formula and a Many-to-One formula for forks. Furthermore, we prove that this auxiliary process characterizes exactly the process of the trait of a uniformly sampled individual in a large population approximation. We detail three examples of growth-fragmentation models: the linear growth model, the exponential growth model and the parasite infection model.


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Aline Marguet. "Uniform sampling in a structured branching population." Bernoulli 25 (4A) 2649 - 2695, November 2019.


Received: 1 September 2016; Revised: 1 July 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110108
MathSciNet: MR4003561
Digital Object Identifier: 10.3150/18-BEJ1066

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability


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Vol.25 • No. 4A • November 2019
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