Limit theorems for one statistic of FBM in the model of real observations

In this article the central limit theorem as Hurst index $H\in\left(0,\frac{3}{4}\right]$ and the non-central limit theorem as Hurst index $H\in\left(\frac{3}{4},1\right)$ for statistics of fraction Brownian motion in the model of real observations are obtained.