Abstract
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.
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Communicated by G. Kallianpur
Research supported by NSF grant MCS8202319.
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Piech, M.A. Brownian motion in infinite dimensional manifolds. Appl Math Optim 13, 251–258 (1985). https://doi.org/10.1007/BF01442210
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DOI: https://doi.org/10.1007/BF01442210