## Electronic Communications in Probability

### On the maximum of the discretely sampled fractional Brownian motion with small Hurst parameter

#### Abstract

We show that the distribution of the maximum of the fractional Brownian motion $B^H$ with Hurst parameter $H\to 0$ 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 $n\to \infty$ slowly enough and the points in $\tau$ are not too close to each other.

#### Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 65, 8 pp.

Dates
Accepted: 30 August 2018
First available in Project Euclid: 18 September 2018

https://projecteuclid.org/euclid.ecp/1537257726

Digital Object Identifier
doi:10.1214/18-ECP167

Mathematical Reviews number (MathSciNet)
MR3863921

Zentralblatt MATH identifier
1401.60061

#### Citation

Borovkov, Konstantin; Zhitlukhin, Mikhail. On the maximum of the discretely sampled fractional Brownian motion with small Hurst parameter. Electron. Commun. Probab. 23 (2018), paper no. 65, 8 pp. doi:10.1214/18-ECP167. https://projecteuclid.org/euclid.ecp/1537257726

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