A simple construction of the fractional Brownian motion. (Q2574625)

The aim of the paper is to construct the fractional Brownian motion with the Hurst parameter \(H\in (0,1)\) as a limit of correlated random walks. Taking a suitable random coefficient of correlation of a random walk on \(\mathbb Z\) and averaging over a large number of walk a discrete Gaussian process is obtained, the scaling limit of which is the fractional Brownian motion. The cases \(0<H<\frac 12\) and \(\frac 12 \leq H<1\) are significantly different.