A stochastic Schumacher diffusion process: Probability characteristics computation and statistical analysis

Abstract

The principal goal of this article is to establish a methodological approach to computational statistical analysis for a new inhomogeneous stochastic diffusion process with mean function corresponds to the Schumacher curve. Firstly, we analyse the principal probabilistic characteristics like the functions of the mean and the transition probability density of the process. So, the parameters estimation appearing in the current process are determined by the maximum likelihood approach with discrete sampling. Finally, so as to provide the performance of the proposed process, we will apply these computational statistical results to simulated data based on a discretization of the analytical expression of the processus by justifying the fit and prediction possibilities.