New and refined bounds for expected maxima of fractional Brownian motion

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 $i{n}^{-1},$ $i=1,\dots ,n.$ 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.

10 pages. Fixed a few minor bugs in the expositions. Slightly amended the title, structure of the paper, acknowledgements and the list of references

References in corpus (2)

• An error bound in the Sudakov-Fernique inequality
• On moments of Pitman estimators: the case of fractional Brownian Motion