10 research outputs found
Estimation of the parameters of a stochastic logistic growth model
We consider a stochastic logistic growth model involving both birth and death
rates in the drift and diffusion coefficients for which extinction eventually
occurs almost surely. The associated complete Fokker-Planck equation describing
the law of the process is established and studied. We then use its solution to
build a likelihood function for the unknown model parameters, when discretely
sampled data is available. The existing estimation methods need adaptation in
order to deal with the extinction problem. We propose such adaptations, based
on the particular form of the Fokker-Planck equation, and we evaluate their
performances with numerical simulations. In the same time, we explore the
identifiability of the parameters which is a crucial problem for the
corresponding deterministic (noise free) model
Approximation of the Fokker-Planck equation of the stochastic chemostat
MAMERN IV--2011: The 4th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources- PART IInternational audienceWe 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
Stochastic models for the chemostat
International audienceThe chemostat is classically represented, at high population scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales: from the small population scale to the scale immediately preceding the one corresponding to the deterministic model. 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, an approximation diffusion allows us to propose a model in the form of a system of stochastic differential equations
Parameter identification for a stochastic logistic growth model with extinction
International audienc
Analysis and Approximation of a Stochastic Growth Model with Extinction
International audienceWe consider a stochastic growth model for which extinction eventually occurs almost surely. The associated complete Fokker–Planck equation describing the law of the process is established and studied. This equation combines a PDE and an ODE, connected one to each other. We then design a finite differences numerical scheme under a probabilistic viewpoint. The model and its approximation are evaluated through numerical simulations