Some properties of fractional Brownian motion

Authors

  • Katsiaryna A. Haitsiukevich Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk
  • Mikalai N. Troush Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

Keywords:

fractional Brownian motion, characteristics of random processes, dependence and independence of process increments

Abstract

This article is dedicated to the study of the characteristics of random processes, with properties of self-similarity and fractality. The study is based on the consideration of numerical characteristics of processes such as mean, variance, covariance, skewness and kurtosis, and the moments and cumulants of higher order, which can then be used to assess the quality and selection of the best simulation algorithm and reseach real-world data. The study was conducted for the random process of fractional Brownian motion, which is widely used. The article also noted that this process has the property of stationary increments, but in general, it increments dependent, which significantly complicates the algorithms used in the modeling process of fractional Brownian motion.

Author Biographies

  • Katsiaryna A. Haitsiukevich, Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

    student at the faculty of applied mathematics and computer science

  • Mikalai N. Troush, Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

    doctor of science (physics and mathematics), full professor; head of the department of theory of probability
    and mathematical statistic, faculty of applied mathematics and computer sciences

References

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Published

2017-12-02

Issue

No. 1 (2017): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Haitsiukevich, K.A. and Troush, M.N. 2017. Some properties of fractional Brownian motion. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Dec. 2017), 23–27.