Integration by Parts and Quasi-Invariance for Heat Kernel Measures on Loop Groups

Journal of Functional Analysis

Volumn 149, Issue 2, 1997, Pages 470-547

  Driver, Bruce K ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000515916     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1997.3103     Document Type: Article

References (24)

1. Bell Denis. A quasi-invariance theorem for measures on Banach spaces. Trans. Amer. Math. Soc. 290:1985;851-855.
2. Cruzeiro Ana-Bela. Équations différentielles ordinaires: Non explosion et mesures quasi-invariantes. J. Functional Anal. 54:1983;193-205.
3. Cruzeiro Ana-Bela. Équations différentielles sur l'espace de Wiener et formules de Cameron-Martin non lineaires. J. Functional Anal. 54:1983;206-227.
4. Driver B. K. A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold. J. Functional Anal. 110:1992;272-376.
5. B. K. Driver, December 1996, Integration by parts for heat kernel measures revisted.
6. Driver B. K., Lohrenz T. Logarithmic Sobolev inequalities for pinned loop groups. J. Functional Anal. 140:1996;381-448.
7. B. K. Driver, L. Gross, 1997, Hilbert spaces of holomorphic functions on complex Lie groups, Proceedings of the 1994 Taniguchi Symposium: New Trends in Stochastic Analysis, 76, 106, World Scientific, New Jersey.
8. Emery M. Stochastic Calculus in Manifolds. 1989;Springer-Verlag, Berlin/Heidelberg/ New York.
9. Folland Gerald B. Real Analysis, Modern Techniques and their Applications. 1984;Wiley, New York.
10. Freed D. S. The geometry of loop groups. J. Diff. Geom. 28:1988;223-276.
11. Gross L. Abstract Wiener Spaces, Proc. 5th Berkeley Symposium Math. Stat. Prob. 2:1965;31-42.
12. Elton, Hsu, Lectures given at the IAS/Park City Mathematics Institute, Institute for Advanced Study.
13. Ikeda N., Watanabe S. Stochastic Differential Equations and Diffusion Processes. 1989;North-Holland, Amsterdam/Oxford/New York.
14. Kunita H. Stochastic Flows and Stochastic Differential Equations. 1990;Cambridge Univ. Press, Cambridge.
15. Kuo H.-H. Gaussian Maesures in Banach Spaces. Lecture Notes in Mathematics. 463:1975;Springer-Verlag, Berlin.
16. Kusuoka S., Stroock D. Precise asymptotics of certain Wiener functionals. J. Functional Anal. 99:1991;1-74.
17. Malliavin P. Hypoellipticity in infinite dimension. Pinsky Mark A. Diffusion Processes and Related Problems in Analysis. Vol. I. Diffusions in Analysis and Geometry. Papers from the International Conference Held at Northwestern University, Evanston, Illinois, October 23-27, 1989. Progress in Probability. 22:1990.
18. Métivier Michel. Semimartingales, a Course on Stochastic Processes. 1982;Gruyter, Berlin/New York.
19. Métivier M., Pellaumail J. Stochastic Intégration. 1980;Academic Press, New York.
20. Peters Gunnar. Anticipating flows on the Wiener space generated by vector fields of low regularity. J. Funct. Anal. 142:1996;129-192.
21. Peters Gunnar. Flows on the Wiener space generated by vector fields with low regularity. C. R. Acad. Sci. Paris Série I. 320:1995;1003-1008.
22. Protter P. Stochastic Integration and Differential Equations; A New Approach. 1990;Springer, Berlin/Heidelberg/New York.
23. Reed Michael, Simon Barry. Methods of Modern Mathematical Physics: I Functional Analysis. 1980;Academic Press, New York.
24. Revuz, Yor. Continuous Martingales and Brownian Motion. 1991;Springer-Verlag, Berlin/Heidelberg/New York.