**6. Conclusions**

This article presents a study of the Gamma Power Stochastic Gompertz Diffusion Process (*γ*-PSGDP), including all its probabilistic properties and the corresponding statistical inference. As a particular case in the limit comparison test, we also study the Gamma Power Stochastic Lognormal Diffusion Process ( *γ*-PSLDP).

A simulation study was conducted, analysing different process trajectories.

In the future, it will be possible to apply these models to fit real data and to obtain goodness of fit results between the processes and the data. We will also study the possibility of defining all these processes in their non-homogeneous form, by introducing exogenous factors, and considering the use of numerical methods to obtain the estimates.

**Author Contributions:** All the authors have collaborated equally in the realization of this work, both in theoretical and applied developments. Similarly in the writing and review of it. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research has been funded by "Programa Operativo FEDER de Andalucía 2014-2020 A-FQM-228-UGR18".

**Conflicts of Interest:** The authors declare no conflict of interest.
