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Modeling oil production and its peak by means of a stochastic diffusion process based on the Hubbert curve

Author

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  • Luz-Sant’Ana, Istoni
  • Román-Román, Patricia
  • Torres-Ruiz, Francisco

Abstract

The present paper introduces a new diffusion process for the purpose of modeling a Hubbert-type behavior pattern. The main features of the process will be analyzed and the maximum likelihood estimation of the parameters will be carried out through discrete sampling. To this end, a complex system of equations must be solved through numerical procedures, requiring the search for an appropriate initial solution. To this end, we propose three search procedures.

Suggested Citation

  • Luz-Sant’Ana, Istoni & Román-Román, Patricia & Torres-Ruiz, Francisco, 2017. "Modeling oil production and its peak by means of a stochastic diffusion process based on the Hubbert curve," Energy, Elsevier, vol. 133(C), pages 455-470.
    • Handle: RePEc:eee:energy:v:133:y:2017:i:c:p:455-470
    DOI: 10.1016/j.energy.2017.05.125
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    Cited by:

    1. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2019. "A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    2. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    3. Antonio Barrera & Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic," Mathematics, MDPI, vol. 9(19), pages 1-29, September.
    4. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "Hyperbolastic Models from a Stochastic Differential Equation Point of View," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    5. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2018. "Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors," Mathematics, MDPI, vol. 6(5), pages 1-13, May.

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