New and refined bounds for expected maxima of fractional Brownian motion

Konstantin Borovkov, Yuliya Mishura, Alexander Novikov and Mikhail Zhitlukhin

Statistics & Probability Letters, 2018, vol. 137, issue C, 142-147

Abstract: For the fractional Brownian motion BH with the Hurst parameter value H in (0,1∕2), we derive new upper and lower bounds for the difference between the expectations of the maximum of BH over [0,1] and the maximum of BH over the discrete set of values in−1, i=1,…,n. We use these results to improve our earlier upper bounds for the expectation of the maximum of BH over [0,1] and derive new upper bounds for Pickands’ constant.

Keywords: Fractional Brownian motion; Convergence rate; Discrete time approximation; Pickands’ constant (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2018.01.025

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