Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion
type: Item
instance of: scholarly article
title: Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion
zbMATH Open document ID: 0983.60052
DOI: 10.1016/S0167-7152(00)00157-7
author: Jean Mémin
author: Yuliya S. Mishura
author: Esko Valkeila
published in: Statistics \& Probability Letters
publication date: 2002-04-02T00:00:00Z
reviewed by: Tomasz Bojdecki
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1599546
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: stochastic integration
zbMATH Keywords: moment inequalities
MaRDI profile type: Publication
cites work: Stochastic and multiple Wiener integrals for Gaussian processes
cites work: An isometric approach to generalized stochastic integrals
cites work: An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
cites work: On some maximal inequalities for fractional Brownian motions
cites work: Are classes of deterministic integrands for fractional Brownian motion on an interval complete?
cites work: Arbitrage with Fractional Brownian Motion
cites work: Q3141895
full work available at URL: s0167-7152(00)00157-7
OpenAlex ID: W2021101842
Wikidata QID: Q128090054
review text: Let \(Z\) be a fractional Brownian motion with Hurst parameter \(H\). For a Wiener-type stochastic integral \(\int fdZ\), properly defined, it is proved that for every \(r>0\) there exists a constant \(c(H,r)\) such that NEWLINE\[NEWLINE E\left |\int_a^bf(u)dZ_u\right |^r \leq c(H,r)||f||^r_{L^{1/H}(a,b)}NEWLINE\]NEWLINE for each \(0\leq a<b<\infty\), provided that \(H>{1\over 2}\). If \(H<{1\over 2}\), then the opposite inequality holds. It is also shown that lower or upper estimates do not hold in the cases \(H>{1\over 2}\) or \(H<{1\over 2}\), respectively.
description: scientific article; zbMATH DE number 1599546