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

2018/02/09 by Konstantin Borovkov, Borovkov, Konstantin, Mikhail Zhitlukhin +1
Economics, Econometrics and Finance · Mathematics · #60E15 #60F05 (Secondary) #60G22 (Primary) 60G15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1802.03496

openalex publication_date 2018/02/09 · openalex created_date 2022/08/21 · openalex updated_date 2026/07/28

Abstract

We show that the distribution of the maximum of the fractional Brownian\nmotion B^H with Hurst parameter H\→ 0 over an n-point set \τ \⊂\n[0,1] can be approximated by the normal law with mean \√(\ln n) and\nvariance 1/2 provided that n\→ \∞ slowly enough and the points in\n\τ are not too close to each other.\n

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