Bounds for expected supremum of fractional Brownian motion with drift

We provide upper and lower bounds for the mean $\mathscr{M}(H)$ of $\sup_{t\geq 0} \{B_H(t) - t\}$ , with $B_H(\!\cdot\!)$ a zero-mean, variance-normalized version of fractional Brownian motion with Hurst parameter $H\in(0,1)$ . We find bounds in (semi-) closed form, distinguishing between $H\in(0,\...

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Veröffentlicht in:	Journal of applied probability 2021-06, Vol.58 (2), p.411-427, Article 0021900220000984
Hauptverfasser:	Bisewski, Krzysztof, Dębicki, Krzysztof, Mandjes, Michel
Format:	Artikel
Sprache:	eng
Schlagworte:	Brownian motion Expected values Lower bounds Mathematics Original Article Physical Sciences Random variables Science & Technology Statistics & Probability Upper bounds
Online-Zugang:	Volltext
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