On some maximal inequalities for fractional Brownian motions
type: Item
instance of: scholarly article
title: On some maximal inequalities for fractional Brownian motions
zbMATH Open document ID: 0947.60033
DOI: 10.1016/S0167-7152(98)00290-9
published in: Statistics \& Probability Letters
publication date: 2000-11-06T00:00:00Z
review text: Let \(Z= (Z_t)_{t\geq 0}\) be a fractional Brownian motion with Hurst index \(H\). Denote by \(F= (F_t)_{t\geq 0}\) the filtration generated by \(Z\). Let \(\tau\) be a stopping time with respect to the filtration \(F\) and \(Z_t^*= \sup_{s\leq t} |Z_s|\). Then for any \(p>0\) and \(H\in (\frac 12,1)\) \[ c_1 E(\tau^{pH})\leq E((Z_\tau^*)^p)\leq c_2 E(\tau^{pH}), \] and for any \(p>0\) and \(H\in (0, \frac 12)\) \[ c_1 E(\tau^{pH})\leq E((Z_\tau^*)^p), \] where the constants \(c_1,c_2> 0\) depend only on the parameters \(p\), \(H\).
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60H99
zbMATH DE Number: 1395118
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: maximal inequalities
author: A. Novikov
author: Esko Valkeila
MaRDI profile type: Publication
Wikidata QID: Q109967583
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full work available at URL: s0167-7152(98)00290-9
OpenAlex ID: W2092576876
description: scientific article; zbMATH DE number 1395118