Geodesic
Some properties of fractional brownian motion
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2017), pp. 23-27
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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.
Keywords: fractional Brownian motion; characteristics of random processes; dependence and independence of process increments. 
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K. Haitsiukevich; N. N. Troush. Some properties of fractional brownian motion. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2017), pp. 23-27. http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a3/

[1] B. B. Mandelbrot, J. W. van-Ness, “Fractional Brownian motion, fractional noises and applications”, SIAM Rev, 10, # 4 (1968), 422–437

[2] G. Samorodnitsky, M. S. Taqqu, “Stable non-Gaussian random processes”, New York, 1994

[3] A. N. Shiryaev, “Osnovy stokhasticheskoi i finansovoi matematiki”, 1998

[4] E. Lakhel, M. A. McKibben, “Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion”, Afr. Mat, 7 (2016), 1–14

[5] T. Dieker, “Simulation of fractional Brownian motion”, CWI and University of Twente Department of Mathematical Sciences. Amsterdam, 2004, 12

[6] I. Norros, “A Storage Model with Self-Similar Input”, Queuing Syst, 16 (1994), 387–396

[7] P. Cheredito, “Arbitrage in fractional Brownian motion models”, Finance Stoch, 7 (2003), 533–553

[8] D. Ilalan, “Elliott wave principle and the corresponding fractional Brownian motion in stock markets: Evidence from Nikkei 225 index”, Chaos, Solitons and Fractals, 92 (2016), 137–141