Besov regularity for the indefinite Skorohod integral with respect to the fractional Brownian motion: The singular case

Abstract

Using the techniques of the Malliavin calculus and the properties of Gaussian processes, we prove that the paths of the indefinite Skorohod integral with respect to the fractional Brownian motion (fBm) with Hurst parameter less than 1/2 belongs to the Besov space B p , X H , for any p >(1/ H ).