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arXiv · 1612.07842

New and refined bounds for expected maxima of fractional Brownian motion

Konstantin Borovkov·Yuliya Mishura·Alexander Novikov·Mikhail Zhitlukhin
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Abstract

For the fractional Brownian motion $B^H$ 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 $B^H$ over [0,1] and the maximum of $B^H$ over the discrete set of values $ in^{-1},$ $i=1,\ldots, n.$ We use these results to improve our earlier upper bounds for the expectation of the maximum of $B^H$ over $[0,1]$ and derive new upper bounds for Pickands' constant.

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Konstantin Borovkov, Yuliya Mishura, Alexander Novikov, Mikhail Zhitlukhin. 2016-12-23. New and refined bounds for expected maxima of fractional Brownian motion. https://arxiv.org/abs/1612.07842

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