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Uniform sampling in a structured branching population

Aline Marguet 1, 2
2 IBIS - Modeling, simulation, measurement, and control of bacterial regulatory networks
LAPM - Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble], Inria Grenoble - Rhône-Alpes, Institut Jean Roget
Abstract : 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 along the spine 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 the 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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Contributor : Aline Marguet <>
Submitted on : Monday, November 19, 2018 - 11:06:14 AM
Last modification on : Wednesday, November 4, 2020 - 3:43:17 PM
Long-term archiving on: : Wednesday, February 20, 2019 - 1:25:14 PM


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Aline Marguet. Uniform sampling in a structured branching population. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2019, 25 (4A), pp.2649-2695. ⟨10.3150/18-BEJ1066⟩. ⟨hal-01362366v4⟩



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