Limit theorems for functions of a fractional Brownian motion
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 42-62
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Sample statistics of samples from a fractional Brownian motion with Hurst exponent $H$, and in particular, autocovariance statistics, are considered. Two statistics characterizing the covariate dependence between the increments of this process are studied; in particular, their asymptotic properties and the limit distributions are examined. Each of the statistics is shown to converge almost everywhere; their limits are evaluated. It is found that these statistics have different limit distributions depending on the value of $H$. A complete description of these distributions in terms of semi-invariants is put forward.
Keywords:
random processes, probability theory, fractional Brownian motion, Hurst exponent, limit theorems.
@article{TVP_2020_65_1_a2,
author = {A. V. Savitskii},
title = {Limit theorems for functions of a fractional {Brownian} motion},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {42--62},
publisher = {mathdoc},
volume = {65},
number = {1},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a2/}
}
A. V. Savitskii. Limit theorems for functions of a fractional Brownian motion. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 42-62. http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a2/