Methods and Algorithms for Simulation Modelling of Fractal Processes

Abstract

The report presents methods and algorithms for simulation modelling of fractal processes. Fractal processes based on fractal Brownian motion, fractal Gaussian noise and, fractal Gaussian noise-wavelet transformation are simulated. Based on the performed comparative analysis of the algorithms for simulation modelling of fractal processes with respect to the accuracy parameter, it follows that the algorithms based on the models of fractal Gaussian noise and fractal Gaussian noise-wavelet transformation have the smallest relative error with respect to the Hurst parameter. The value of the Hurst parameter is one of the most important characteristics determining the degree of self-similarity of fractal processes. The considered algorithms based on these two models can be applied for modelling of physiological data, including cardiological data, because they have fractal properties.