  In this article we present an intrinsec construction of foliated Brownian
motion via stochastic calculus adapted to foliation. The stochastic approach
together with a proposed foliated vector calculus provide a natural method to
work on harmonic measures. Other results include a decomposition of the
Laplacian in terms of the foliated and basic Laplacians, a characterization of
totally invariant measures and a differential equation for the density of
harmonic measures.
