Hyperbolastic Models from a Stochastic Differential Equation Point of View Barrera, Antonio Román Román, Patricia Torres Ruiz, Francisco De Asís Stochastic diffusion process Stochastic differential equations Hyperbolastic curves This work was supported in part by the Ministerio de Economia, Industria y Competitividad, Spain, under Grant MTM2017-85568-P and by the FEDER, Consejeria de Economia y Conocimiento de la Junta de Andalucia, Spain under Grant A-FQM-456-UGR18. 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. 2021-10-07T10:27:30Z 2021-10-07T10:27:30Z 2021-08-04 info:eu-repo/semantics/article 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] http://hdl.handle.net/10481/70717 10.3390/math9161835 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI