New and refined bounds for expected maxima of fractional Brownian motion

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Journal Article
Statistics and Probability Letters, 2018, 137 pp. 142 - 147
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© 2018 Elsevier B.V. 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.
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