Open AccessSimulation of a strictly φ-sub-Gaussian generalized fractional Brownian motion
Author(s) -
Olga Vasylyk,
I. I. Lovytska
Publication year - 2021
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2021/1.1
Subject(s) - fractional brownian motion , mathematics , hurst exponent , gaussian process , gaussian , brownian motion , brownian excursion , statistical physics , diffusion process , stochastic process , representation (politics) , wiener process , reflected brownian motion , heavy traffic approximation , mathematical analysis , geometric brownian motion , discrete mathematics , physics , statistics , computer science , quantum mechanics , knowledge management , politics , political science , law , innovation diffusion
In the paper, we consider the problem of simulation of a strictly φ-sub-Gaussian generalized fractional Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly φ-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when φ(x) = (|x|^p)/p, |x| ≥ 1, p > 1. In order to obtain these results, we use some results from the theory of φ-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.