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Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

Author

Listed:
  • Antonio Barrera

    (Departamento de Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada, Facultad de Ciencias, Universidad de Málaga, Bulevar Louis Pasteur, 31, 29010 Málaga, Spain
    These authors contributed equally to this work.)

  • Patricia Román-Román

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    Instituto de Matemáticas de la Universidad de Granada (IEMath-GR), Calle Ventanilla 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

  • Francisco Torres-Ruiz

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    Instituto de Matemáticas de la Universidad de Granada (IEMath-GR), Calle Ventanilla 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

Abstract

Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out.

Suggested Citation

  • Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2020. "Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior," Mathematics, MDPI, vol. 8(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:155-:d:311859
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    2. 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.

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