Section: New Results

Stochastic growth model with extinction

Participant : Fabien Campillo.

In collaboration with Marc Joannides and Irène Larramendy-Valverde (IMAG / Université de Montpellier), we consider in [6] a stochastic logistic growth model given by a stochastic differential equation featuring both birth and death rates in the drift and diffusion coefficients. Our aim is to infer these rates, based on discrete observations with possible extinction. Since extinction occurs eventually for the model, the density of the diffusion process is not absolutely continuous with respect to the Lebesgue measure; we established the associated Fokker-Planck equation together with appropriate numerical schemes. This formulation allows to design variants of the standard methods that can handle extinction.