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Analysis and Approximation of a Stochastic Growth Model with Extinction

Author

Listed:
  • Fabien Campillo

    (Project-Team MODEMIC, INRIA/INRA, UMR MISTEA)

  • Marc Joannides

    (Project-Team MODEMIC, INRIA/INRA, UMR MISTEA
    Université Montpellier 2/I3M)

  • Irène Larramendy-Valverde

    (Université Montpellier 2/I3M)

Abstract

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.

Suggested Citation

  • Fabien Campillo & Marc Joannides & Irène Larramendy-Valverde, 2016. "Analysis and Approximation of a Stochastic Growth Model with Extinction," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 499-515, June.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:2:d:10.1007_s11009-015-9438-7
    DOI: 10.1007/s11009-015-9438-7
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    References listed on IDEAS

    as
    1. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    2. Christos H. Skiadas, 2010. "Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 261-270, June.
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    Cited by:

    1. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez & Eva Ramos-Ábalos, 2020. "Stochastic Square of the Brennan-Schwartz Diffusion Process: Statistical Computation and Application," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 455-476, June.
    2. Zhang, Xiaofeng & Yuan, Rong, 2021. "Forward attractor for stochastic chemostat model with multiplicative noise," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).

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