Inference in the stochastic Gompertz diffusion model with continuous sampling

• Autores: Ramón Gutiérrez Jáimez , Ahmed Nafidi , Ramón Gutiérrez Sánchez
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques :Jaca, Spain, September 15-17, 2003 / coord. por Manuel Pedro Palacios Latasa , David Trujillo, Juan José Torrens, Monique Madaune-Tort, María Cruz López de Silanes Busto , Gerardo Sanz Sáiz , 2003, ISBN 84-7733-720-9 , págs. 347-353
• Recoge los contenidos presentados a: Jornadas Zaragoza-Pau de Matemática Aplicada y Estadística (8. 2003. Jaca)
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• Resumen

  • In the present paper, we approach the stochastic Gompertz diffusion process (SGDP) from the point of view of Itô's stochastic differential equations. The stochastic model is solved analytically by applying Itô's calculus and the mean value of the proposed process is calculated. The parameter estimators are then derived by means of two procedures: the first is used to estimate the parameters in the drift coefficient by the maximum likelihood principle, based on continuous sampling, and the second procedure approximates the diffusion coefficient. Finally, a simulation of the process is presented. Thus, a typical simulated trajectory of the process and its estimators is obtained.