Modeling and fitting by a modified stochastic logistic diffusion model, parameter estimation and application

This article introduces an innovative stochastic diffusion process with relation to a new formulation of the logistic curve and explores the use of simulated annealing to estimate by maximum likelihood the process parameters. At first, the principal characteristics of the process are determined, notably the probability density and mean functions. Next, the parameters estimation is done by the maximum likelihood technique with the use of discrete sampling. For this purpose, the simulated annealing method is applied after bounding the parameters domain by a step-by-step approach. Finally, in order to justify this approach, we enclose the results obtained by different simulation examples, and we give an application related to an example of a microorganism growth.