Electronic Communications in Probability

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

Konstantin Borovkov and Mikhail Zhitlukhin

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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

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

Received: 14 February 2018
Accepted: 30 August 2018
First available in Project Euclid: 18 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

fractional Brownian motion maxima discrete sampling normal approximation

Creative Commons Attribution 4.0 International License.


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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