On the maximum of the discretely sampled fractional Brownian motion with small Hurst parameter. (English) Zbl 1401.60061

Summary: We show that the distribution of the maximum of the fractional Brownian motion \(B^H\) with Hurst parameter \(H\rightarrow 0\) over an \(n\)-point set \(\tau \subset [0,1]\) can be approximated by the normal law with mean \(\sqrt{\ln n} \) and variance \(1/2\) provided that \(n\rightarrow \infty\) slowly enough and the points in \(\tau \) are not too close to each other.


60G22 Fractional processes, including fractional Brownian motion
60G15 Gaussian processes
60E15 Inequalities; stochastic orderings
60F05 Central limit and other weak theorems
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