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A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation

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  • Nafidi, Ahmed
  • El Azri, Abdenbi

Abstract

Stochastic diffusion models have extensive areas of applications. They have been the object of particular attention in diverse fields of science such as biology, physics, chemistry, medical science and mathematical finance. In this paper, we present a new non-homogeneous stochastic diffusion process, in which the mean function is proportional to the growth curve of the Lundqvist–Korf. We first analyze the main features of the process including the transition probability density function and the mean functions. We then estimate the parameters of the model by the maximum likelihood method using discrete sampling after which we propose the simulated annealing algorithm to solve the likelihood equations. Finally, in order to highlight the utility of this methodology, we include the results obtained from several examples of simulation.

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  • Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:25-38
    DOI: 10.1016/j.matcom.2020.10.022
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    1. R. Gutiérrez & R. Gutiérrez‐Sánchez & A. Nafidi, 2009. "Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 385-405, May.
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    6. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
    7. Vera, J. Fernando & Di­az-Garci­a, Jose A., 2008. "A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5055-5065, August.
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    9. Nafidi, A. & Bahij, M. & Achchab, B. & Gutiérrez-Sanchez, R., 2019. "The stochastic Weibull diffusion process: Computational aspects and simulation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 575-587.
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