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Diffusions on path and loop spaces: existence, finite dimensional approximation and Hölder continuity
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  • Published: September 1997

Diffusions on path and loop spaces: existence, finite dimensional approximation and Hölder continuity

  • Andreas Eberle1 

Probability Theory and Related Fields volume 109, pages 77–99 (1997)Cite this article

  • 111 Accesses

  • 12 Citations

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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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  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, D-33501 Bielefeld, Germany (eberle@mathematik.uni-bielefeld.de), , , , , , DE

    Andreas Eberle

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  1. Andreas Eberle
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Received: 6 September 1996 / In revised form: 1 April 1997

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Cite this article

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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  • Issue Date: September 1997

  • DOI: https://doi.org/10.1007/s004400050126

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  • AMS Subject Classification (1996): Primary: 58G32. Secondary: 60J60
  • 60G17
  • 60B10
  • 31C25
  • 58B99
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