Statistical analysis of growth-fragmentation models

Abstract : This work is concerned with growth-fragmentation models, implemented for investigating the growth of a population of cells which divide according to an unknown splitting rate, depending on a structuring variable – age and size being the two paradigmatic examples. The mathematical framework includes statistics of processes, nonparametric estimations and analysis of partial differential equations. The three objectives of this work are the following : get a nonparametric estimate of the division rate (as a function of age or size) for different observation schemes (genealogical or continuous) ; to study the transmission of a biological feature from one cell to an other and study the feature of one typical cell ; to compare different populations of cells through their Malthus parameter, which governs the global growth (when introducing variability in the growth rate among cells for instance).
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Submitted on : Sunday, November 29, 2015 - 7:12:57 PM
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Adelaïde Olivier. Statistical analysis of growth-fragmentation models. Statistics [math.ST]. Université Paris Dauphine - Paris IX, 2015. English. ⟨NNT : 2015PA090047⟩. ⟨tel-01235239⟩

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