Stochastic Models for the Chemostat
Résumé
The chemostat is classically represented, at high popula- tion scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales. At a microscopic scale we present a pure jump stochastic model that gives rise, at the macroscopic scale, to the ordinary differential equation model. At an intermediate scale, a diffusion approximation allows us to propose a model in the form of a system of stochastic differential equations.