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A differentiable isomorphism between Wiener space and path group

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1655)

Abstract

Given a compact Lie group G endowed with, its left invariant Cartan connection, we consider the path space P over G and its Wiener measure P. It is known that there exists a differentiable measurable isomorphism I between the classical Wiener space (W, μ) and (P, P). See [A], [D], [S2], [PU], [G].

In this article, using the pull-back by I we establish the De Rham-Hodge-Kodaira decomposition theorem on (Λ(P)P).

Keywords

  • Loop Group
  • Path Space
  • Wiener Space
  • Wiener Measure
  • Hilbertian Basis

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© 1997 Springer-Verlag Berlin Heidelberg

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Fang, S., Franchi, J. (1997). A differentiable isomorphism between Wiener space and path group. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119291

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  • DOI: https://doi.org/10.1007/BFb0119291

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  • Print ISBN: 978-3-540-62634-3

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