A stochastic log-logistic diffusion process: Statistical computational aspects and application to real data

Abstract

This article introduces a new stochastic diffusion process based on the theory of diffusion processes whose mean function is proportional to the log-logistic growth curve. The main characteristics of the process are analyzed, including the transition probability density function, the mean functions and in particular, the auto-correlation function between two times of the process. The parameters of the process are estimated by maximum likelihood method using discrete sampling. The simulated annealing algorithm is applied after bounding the parametric space by a strategy procedure to solve the likelihood equations. The behavior of the diffusion process here derived is finally applied to study an example for the growth data of a microorganism culture.