Journal article
On the maximum of the discretely sampled fractional Brownian motion with small hurst parameter
K Borovkov, M Zhitlukhin
Electronic Communications in Probability | UNIV WASHINGTON, DEPT MATHEMATICS | Published : 2018
DOI: 10.1214/18-ECP167
Abstract
We show that the distribution of the maximum of the fractional Brownian motion BH with Hurst parameter H√→ 0 over an n-point set τ ⊂ [0, 1] can be approximated by the normal law with mean ln n and variance 1/2 provided that n → ∞ slowly enough and the points in τ are not too close to each other.
Grants
Awarded by Australian Research Council
Funding Acknowledgements
Some of the presented results were obtained when the authors were taking part in the "Mathematics of Risk" program ran at the MATRIX Research Institute in 2017. We are grateful to MATRIX for its support and hospitality. The authors are also grateful to the anonymous referee whose comments helped to improve the exposition of this paper.