A differentiable isomorphism between Wiener space and path group

Shizan Fang; Jacques Franchi

Séminaire de probabilités de Strasbourg (1997)

  • Volume: 31, page 54-61

How to cite


Fang, Shizan, and Franchi, Jacques. "A differentiable isomorphism between Wiener space and path group." Séminaire de probabilités de Strasbourg 31 (1997): 54-61. <http://eudml.org/doc/113972>.

author = {Fang, Shizan, Franchi, Jacques},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {path space; Wiener space; Hodge decomposition},
language = {fre},
pages = {54-61},
publisher = {Springer - Lecture Notes in Mathematics},
title = {A differentiable isomorphism between Wiener space and path group},
url = {http://eudml.org/doc/113972},
volume = {31},
year = {1997},

AU - Fang, Shizan
AU - Franchi, Jacques
TI - A differentiable isomorphism between Wiener space and path group
JO - Séminaire de probabilités de Strasbourg
PY - 1997
PB - Springer - Lecture Notes in Mathematics
VL - 31
SP - 54
EP - 61
LA - fre
KW - path space; Wiener space; Hodge decomposition
UR - http://eudml.org/doc/113972
ER -


  1. [A] Aida S.Sobolev spaces over loop groups. J.F.A.127, p. 155-172, 1995. Zbl0823.46034MR1308620
  2. [AM] Arai A. and Mitoma I.De Rham-Hodge-Kodaira decomposition in infinite dimension. Math. Ann.291, p. 51-73, 1991. Zbl0762.58004MR1125007
  3. [D] Driver B.The non-equivalence of Dirichlet forms on path spaces. Stochastic Analysis on Infinite Dimensional Spaces, p. 75-87, Proceedings Baton Rouge 1994, H. Kunita and H.H. Kuo ed. Zbl0819.31005MR1415660
  4. [FF1] Fang S. and Franchi J.Platitude de la structure riemannienne sur les groupes de chemins et identité d'énergie pour les intégrales stochastiques. C.R.A.S.Paris, t. 321, S.1, p. 1371-1376, 1995. Zbl0846.60058MR1363583
  5. [FF2] Fang S. and Franchi J.Flatness of the path group over a compact Lie group and Shigekawa identity. Prepublication n° 310 du laboratoire de probabilités de Paris VI, 1995. MR1363583
  6. [FF3] Fang S. and Franchi J.De Rham-Hodge-Kodaira operator on loop groups. Prepublication n° 341 du laboratoire de probabilités de Paris VI, 1996. MR1469347
  7. [G] Gross L.Uniqueness of ground states for Schrödinger operators over loop groups. J.F.A.112, p. 373-441, 1993. Zbl0774.60059MR1213144
  8. [L] Leandre R.Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces. J. Geom. Phys.11, p. 517-528, 1993. Zbl0786.60074MR1230447
  9. [LR] Leandre R. and Roan S.S.A stochastic approach to the Euler-Poincaré number of the loop space over a developpable orbifold. J. Geom. Phys.16, p. 71-98, 1995. Zbl0822.60057MR1325163
  10. [M] Malliavin P.Hypoellipticity in infinite dimension. Diffusion processes and related problems in Analysis, vol. 1, Progress in Probability32, p. 17-33, M. Pinsky ed., Birkhäuser1991. Zbl0723.60059MR1110154
  11. [MM] Malliavin P. and Malliavin M.P.Integration on loop groups I : Quasi invariant measures. J.F.A.93, p. 207-237, 1990. Zbl0715.22024MR1070039
  12. [PU] Pontier M. and Ustunel A.S.Analyse stochastique sur l'espace de Lie-Wiener. C.R.A.S.313, p. 313-316, 1991. Zbl0734.60062MR1126404
  13. [S1] Shigekawa I.De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space. J. Math. Kyoto Univ.26-2, p. 191-202, 1986. Zbl0611.58006MR849215
  14. [S2] Shigekawa I.A quasi homeomorphism on the Wiener space. Proceedings of symposia in pure mathematics57, Stochastic Analysis, p. 473-486, M. Cranston and M. Pinsky ed., 1995. Zbl0821.60059MR1335491

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