Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior
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Diffusion processesGrowth modelOscillabolastic curveStochastic differential equations
Barrera, A.; Román-Román, P.; Torres-Ruiz, F. Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior. Mathematics 2020, 8, 155. [doi:10.3390/math8020155]
SponsorshipThis work was supported in part by the Ministerio de Economía, Industria y Competitividad, Spain, under Grant MTM2017-85568-P and by the Consejería de Economía y Conocimiento de la Junta de Andalucía, Spain under Grant A-FQM-456-UGR18.
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.