Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data

https://doi.org/10.32996/jmss.2021.2.1.1

Authors

  • Ahmed Nafidi Hassan First University of Settat, National School of Applied Sciences, Department of Mathematics and Informatics, LAMSAD, B.P. 280, 26100 Berrechid, Morocco
  • Oussama Rida Hassan First University of Settat, National School of Applied Sciences, Department of Mathematics and Informatics, LAMSAD, B.P. 280, 26100 Berrechid, Morocco
  • Boujemaa Achchab Hassan First University of Settat, National School of Applied Sciences, Department of Mathematics and Informatics, LAMSAD, B.P. 280, 26100 Berrechid, Morocco

Keywords:

Stochastic differential equation, Generalized Brody curve, Maximum likelihood, Optimization algorithms, Simulation, life expectancy

Abstract

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.

Downloads

Download data is not yet available.
Dimensions

Published

2021-01-16

How to Cite

Nafidi, A., Rida, O., & Achchab, B. (2021). Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data . Journal of Mathematics and Statistics Studies, 2(1), 01-11. https://doi.org/10.32996/jmss.2021.2.1.1