2016/09/26 by Bertrand Cloez, Cloez, Bertrand, Coralie Fritsch +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1609.07951
openalex publication_date 2016/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In a chemostat, bacteria live in a growth container of constant volume in\nwhich liquid is injected continuously. Recently, Campillo and Fritsch\nintroduced a mass-structured individual-based model to represent this dynamics\nand proved its convergence to a more classic partial differential equation. In\nthis work, we are interested in the convergence of the fluctuation process. We\nconsider this process in some Sobolev spaces and use central limit theorems on\nHilbert space to prove its convergence in law to an infinite-dimensional\nGaussian process.As a consequence, we obtain a two-dimensional Gaussian\napproximation of the Crump-Young model for which the long time behavior is\nrelatively misunderstood. For this approximation, we derive the invariant\ndistribution and the convergence to it. We also present numerical simulations\nillustrating our results.\n