Abstract
In this article we present an intrinsic construction of foliated Brownian motion (FoBM) via stochastic calculus adapted to a foliated Riemannian manifold ( M , F ) (M, \mathcal {F}) . The stochastic approach together with this proposed foliated vector calculus provide a natural method to work with (L. Garnett’s) harmonic measures in M M . New results include, beside an explicit stochastic equation for the FoBM, a decomposition of the Laplacian of M M in terms of the foliated and the basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
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