The main objective of this paper is to study the possibility of using a stochastic non-homogeneous (without exogenous factors) diffusion process to model the evolution of CO 2 in Morocco. Concretely, we use a new process, in which the trend function is proportional to the modified Lundqvist korf growth curve. First, we study the main characteristics of the process. Moreover, we establish a computational statistical methodology based on the maximum likelihood estimation method and the trend functions. Otherwise, when we estimate the parameters of the model, we obtain a nonlinear equation. Hence, we propose the simulated annealing method to solve it after bounding the parametric space by a stagewise procedure. Also, we include the results obtained from several examples of simulation to validate this methodology. Finally, we apply the process and the methodology established before to real data corresponding to the evolution of CO 2 emissions in Morocco. [ABSTRACT FROM AUTHOR]