Brownian motion in infinite dimensional manifolds

We discuss the extension to infinite dimensional Riemannian-Wiener manifolds of the transport approximation to Brownian motion, which was formulated by M. Pinsky for finite dimensional manifolds. A global representation is given for the Laplace-Beltrami operator in terms of the Riemannian spray and a homogenizing operator based upon the central hitting measure of the surface of the unit ball with respect to the Brownian motion on the model space.