Optimization of the model of ϕ-sub-Gaussian generalized fractional Brownian motion

Simulation methods for stochastic processes are used in many scientific areas, and special attention is given to the fractional Brownian motion. There are many results on simulation of Gaussian fractional Brownian motion. In this paper, we consider simulation of processes from more general class, namely, simulation of a strictly ϕ-sub-Gaussian generalized fractional Brownian motion defined on the finite domain [0,1]. In the beginning of the article, we presented preliminary information which is necessary for understanding the results of our study. In the main part of our paper, for the strictly ϕ-sub-Gaussian generalized fractional Brownian motion with some given function ϕ optimal values of the parameters necessary for simulation with given reliability and accuracy in the space C([0;1]) are found. This gives us a significant reduction in the number of terms needed to ensure the reliability and accuracy of our model. Also, in the paper some results of calculations and simulation are given. As expected, in our case the obtained values of terms in the model are significantly smaller than the corresponding numbers for the models with the values of parameters that are not optimal.