Analysis and Approximation of a Stochastic Growth Model with Extinction

  • Fabien Campillo
  • Marc Joannides
  • Irène Larramendy-Valverde


We 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.


Logistic model Markov processes Diffusion processes Extinction Fokker–Planck equation PDE 

Mathematics Subject Classification (2010)

60J60 60H35 65C20 92D40 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Fabien Campillo
    • 1
  • Marc Joannides
    • 1
    • 2
  • Irène Larramendy-Valverde
    • 2
  1. 1.Project-Team MODEMIC, INRIA/INRA, UMR MISTEAMontpellier cedex 06France
  2. 2.Université Montpellier 2/I3MMontpellier cedex 5France

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