N. S. Aiubava, “Limit theorems for one statistic of FBM in the model of real observations”, Theory Stoch. Process., 2019, Volume 24(40), Issue 1,Pages <nobr>1

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

N. S. Aiubava

Kyiv National Taras Shevchenko University, Mechanics and Mathematics Faculty, Department of Mathematical Analysis, Volodymyrs'ka Street 64, 01601 Kyiv, Ukraine

Abstract: 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.

Keywords: Fractional Brownian motion, weak convergency, central limit theorem, Hurst parameter.

MSC: Primary 60F05; Secondary 60G15

Language: English