Analysis of simulation methods for fractional Brownian motion in the problems of intelligent systems design
Anatolii O. Pashko, Olga V. Lukovych, Iryna V. Rozora, Tetiana Oleshko, Olga Vasylyk · 2019 IEEE International Conference on Advanced Trends in Information Theory (ATIT) · 2019
Statistical modeling algorithms are often used to develop intelligent systems for solving complex problems. When solving problems in the field of economics, financial mathematics, designing of telecommunication networks, models of fractional Brownian motion can be used. In this article different methods of statistical simulation of fractional Brownian motion (FBM) with accuracy and reliability are investigated. The methods are based on the spectral presentation of the FBM, Dzhaparidze and Zanten expansion, Kahrunen transform and on the stationary increments. The developed methods are used for modeling of self-similar traffic and loading process of telecommunication networks.