Summary.
We construct Ornstein–Uhlenbeck processes and more general diffusion processes on path and loop spaces of Riemannian manifolds by finite dimensional approximation. We also show Hölder continuity of the sample paths w.r.t. the supremum norm. The proofs are based on the Lyons–Zheng decomposition.
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Received: 6 September 1996 / In revised form: 1 April 1997
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Eberle, A. Diffusions on path and loop spaces: existence, finite dimensional approximation and Hölder continuity. Probab Theory Relat Fields 109, 77–99 (1997). https://doi.org/10.1007/s004400050126
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DOI: https://doi.org/10.1007/s004400050126