  By using Malliavin calculus and multiple Wiener-It\^o 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 Watanabe space.
