Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion
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.
scientific article; zbMATH DE number 1599546