Hyperbolastic Models from a Stochastic Differential Equation Point of View

Antonio Barrera, Patricia Román-Román and Francisco Torres-Ruiz
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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
Patricia Román-Román: Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla 11, 18001 Granada, Spain
Francisco Torres-Ruiz: Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla 11, 18001 Granada, Spain

Mathematics, 2021, vol. 9, issue 16, 1-18

Abstract: A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

Keywords: stochastic diffusion processes; stochastic differential equations; hyperbolastic curves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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