Uniform sampling in a structured branching population

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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01362366
Contributeur : Aline Marguet <>
Soumis le : dimanche 24 septembre 2017 - 19:25:00
Dernière modification le : mercredi 25 avril 2018 - 10:45:37
Document(s) archivé(s) le : lundi 25 décembre 2017 - 21:33:02

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  • HAL Id : hal-01362366, version 2
  • ARXIV : 1609.05678

Citation

Aline Marguet. Uniform sampling in a structured branching population. 2017. 〈hal-01362366v2〉

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