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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1537257726

Digital Object Identifier
doi:10.1214/18-ECP167

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

Keywords
fractional Brownian motion maxima discrete sampling normal approximation

Rights
Creative Commons Attribution 4.0 International License.

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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References

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