z-logo
open-access-imgOpen Access
Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data
Author(s) -
Ahmed Nafidi,
Oussama Rida,
Boujemâa Achchab
Publication year - 2021
Publication title -
journal of mathematics and statistics studies
Language(s) - English
Resource type - Journals
ISSN - 2709-4200
DOI - 10.32996/jmss.2021.2.1.1
Subject(s) - mathematics , stochastic differential equation , conditional probability distribution , diffusion process , simulated annealing , mathematical optimization , probability density function , stochastic process , probabilistic logic , log normal distribution , computer science , statistics , knowledge management , innovation diffusion
A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.
Having issues? You can contact us here