A τ-Power Stochastic Rayleigh Diffusion Model: Computational Aspects, Simulation and Predictive Analysis

Abstract The overall idea of this paper is to introduce a new family of inhomogeneous stochastic Rayleigh diffusion processes and use them to predict and forecast simulated data after establishing the main characteristics of these kinds of processes. They are interesting models for infectious diseases, health and renewable energies. First of all, we define the new processes by means of a τ-power of the stochastic Rayleigh diffusion model. Then the most important features of the process are examined, with particular attention to its analytic expression, transition probability density function and mean functions. Otherwise, the parameters that appear in the present model are estimated by maximum likelihood with discrete sampling. Lastly, in order to assess the quality of this process, we will use these statistical computations for simulated examples, specifying fitting and prediction possibilities.