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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.

MSC:

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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References:

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