New and refined bounds for expected maxima of fractional Brownian motion
Alexander Novikov and
Statistics & Probability Letters, 2018, vol. 137, issue C, 142-147
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)
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