Approximation of the Fokker-Planck equation of the stochastic chemostat

2011/11/24 by Fabien Campillo, Campillo, Fabien, Marc Joannides +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1111.5716

arxiv created 2011/11/24 · arxiv updated 2011/11/28

Abstract

We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker-Planck associated with this diffusion process, in particular we describe the boundary conditions that modelize the washout. We propose an adapted finite difference scheme for the approximation of the solution of the Fokker-Planck equation.

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