Brownian and fractional Brownian stochastic currents via Malliavin calculus

By using Malliavin calculus and multiple Wiener–Itô integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces with its regularity in the Watanabe spaces.