Statistical analysis of growth-fragmentation models.

Summary This theoretical study is closely linked to a field of application: it consists in modeling the growth of a population of cells which divide according to an unknown rate of division, depending on a so-called structuring variable - age and cell size being the two paradigmatic examples studied. The related mathematical field is at the interface of process statistics, non-parametric estimation and partial differential equation analysis. The three objectives of this work are: to reconstruct the division rate (as a function of age or size) for different observation schemes (in genealogical time or in continuous time) . to study the transmission of a general biological trait from one cell to another and to study the trait of a typical cell . to compare the growth of different populations of cells through the Malthus parameter (after introducing variability in the growth rate for example).