Invariance of 0-currents under diffusions

Abstract

We study two actions of a stochastic flow psi(t) on the space of 0-currents T of a differentiable manifold M. In particular, we give conditions on a current T to be invariant under these actions. Also, we apply our results to the case of 0-currents that come from harmonic measures associated to certain type of foliations on homogeneous spaces.