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

Electronic Communications in Probability

Konstantin Borovkov¹ 

关键词: fractional Brownian motion;    maxima;    discrete sampling;    normal approximation;   

DOI  :  10.1214/18-ECP167

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

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.

【 授权许可】

CC BY