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

DOI10.1214/18-ECP167zbMath1401.60061arXiv1802.03496OpenAlexW2964314882MaRDI QIDQ1990032

Mikhail Zhitlukhin, Konstantin A. Borovkov

Publication date: 24 October 2018

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.03496

zbMATH Keywords

fractional Brownian motionmaximanormal approximationdiscrete sampling

Mathematics Subject Classification ID

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

Cites Work

• On the norming constants for normal maxima
• Stochastic calculus for fractional Brownian motion and related processes.
• Bounds for expected maxima of Gaussian processes and their discrete approximations
• On the rate of convergence of normal extremes
• Volatility is rough
• Pricing under rough volatility

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