Hyperbolastic Models from a Stochastic Differential Equation Point of View
Metadata
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MDPI
Materia
Stochastic diffusion process Stochastic differential equations Hyperbolastic curves
Date
2021-08-04Referencia bibliográfica
Barrera, A.; Román-Román, P.; Torres-Ruiz, F. Hyperbolastic Models from a Stochastic Differential Equation Point of View. Mathematics 2021, 9, 1835. [https://doi.org/10.3390/math9161835]
Sponsorship
Ministerio de Economia, Industria y Competitividad, Spain MTM2017-85568-P; FEDER, Consejeria de Economia y Conocimiento de la Junta de Andalucia, Spain A-FQM-456-UGR18Abstract
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.