Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation
Metadatos
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Materia
Powers of stochastic Gompertz diffusion models Powers of stochastic lognormal diffusion models Estimation in diffusion process Stationary distribution and ergodicity Trend function Application to simulated data
Date
2020-04Referencia bibliográfica
Ramos-Ábalos, E. M., Gutiérrez-Sánchez, R., & Nafidi, A. (2020). Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation. Mathematics, 8(4), 588. [doi:10.3390/math8040588]
Patrocinador
This research has been funded by “Programa Operativo FEDER de Andalucía 2014-2020 A-FQM228-UGR18”Résumé
In this paper, we study a new family of Gompertz processes, defined by the power
of the homogeneous Gompertz diffusion process, which we term the powers of the stochastic
Gompertz diffusion process. First, we show that this homogenous Gompertz diffusion process
is stable, by power transformation, and determine the probabilistic characteristics of the process,
i.e., its analytic expression, the transition probability density function and the trend functions. We then
study the statistical inference in this process. The parameters present in the model are studied by
using the maximum likelihood estimation method, based on discrete sampling, thus obtaining the
expression of the likelihood estimators and their ergodic properties. We then obtain the power process
of the stochastic lognormal diffusion as the limit of the Gompertz process being studied and go on to
obtain all the probabilistic characteristics and the statistical inference. Finally, the proposed model is
applied to simulated data.