## 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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