Equivalence of heat kernel measure and pinned Wiener measure on loop groups;Équivalence entre la mesure de la chaleur et la mesure du pont brownien sur des groupes de lacets

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 331, Issue 9, 2000, Pages 709-712

  Aida, Shigeki ^a   Driver, Bruce K ^b  

^a OSAKA UNIVERSITY   (Japan)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034311789     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(00)01725-0     Document Type: Article

References (12)

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3. Baxendale P., Wiener processes on manifolds of maps, Proc. Roy. Soc. Edinburgh Sect. A 87 (1-2) (1980/81) 127-152.
4. Driver B.K., Integration by parts and quasi-invariance for heat kernel measures on loop groups, J. Funct. Anal. 149 (2) (1997) 470-547.
5. Driver B.K., Lohrenz T., Logarithmic Sobolev inequalities for pinned loop groups, J. Funct. Anal. 140 (2) (1996) 381-448.
6. Driver B.K., Srimurthy V., Absolute continuity of heat kernel measure with respect to pinned Wiener measure on loop groups, UCSD Preprint, 2000; The Annale of Probab. (to appear).
7. Gross L., Logarithmic Sobolev inequalities on loop groups, J. Funct. Anal. 102 (2) (1991) 268-313.
8. Gross L., Uniqueness of ground states for Schrödinger operators over loop groups, J. Funct. Anal. 112 (2) (1993) 373-441.
9. Malliavin M.-P., Malliavin P., Integration on loop groups, I. Quasi-invariant measures, J. Funct. Anal. 93 (1) (1990) 207-237.
10. Malliavin P., Hypoellipticity in Infinite Dimensions, Diffusion Processes and Related Problems in Analysis, Vol. I (Evanston, IL, 1989), Birkhäuser Boston, Boston, MA, 1990, pp. 17-31.
11. Shigekawa I., Transformations of the Brownian Motion on the Lie Group, Stochastic Analysis (katata/Kyoto, 1982), North-Holland, Amsterdam, 1984, pp. 409-422.
12. Srimurthy V., On the equivalence of measures on loop spaces, Probab. Theory Relat. Fields (2000) (to appear).