Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

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: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
Francisco Torres-Ruiz: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain

Mathematics, 2020, vol. 8, issue 2, 1-20

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.

Keywords: diffusion processes; growth model; oscillabolastic curve; stochastic differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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