Some properties of fractional brownian motion

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.