Geodesic
Limit theorems for functions of a fractional Brownian motion
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 42-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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