A class of vector fields on path spaces

Journal of Functional Analysis

Volumn 145, Issue 1, 1997, Pages 205-223

  Lyons, T J ^a   Qian, Z M ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031116239     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.3013     Document Type: Article

References (32)

1. Albeverio S., Hoegh-Krohn R. The energy representation of Sobolev Lie groups. Compositio Math. 36:1978;37-52.
2. Bismut J.-M. Large Deviations and the Malliavin Calculus. 1984;Birkhäuser, Boston/Basel/Stuttgart.
3. Cameron R. H., Martin W. T. Transformations of Wiener integrals under translations. Ann. of Math. 45:1944;386-386.
4. Cameron R. H., Martin W. T. Transformations of Wiener integrals under a general class of linear transformations. Trans. Amer. Math. Soc. 58:1945;184-219.
5. Cameron R. H., Martin W. T. The transformation of Wiener integrals by nonlinear transformations. Trans. Amer. Math. Soc. 66:1949;253-283.
6. Cruzeiro A. B. Equations différentielles sur l'espace de Wiener et formules de Cameron-Martin non linéaires. J. Funct. Anal. 54:1983;206-227.
7. Driver B. A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold. J. Funct. Anal. 110:1992;273-376.
8. Driver B. Towards calculus and geometry on path spaces. Proc. Sympos. Pure Math. 57:1995;405-422.
9. B. Driver, 1995, A primer on Riemannian geometry and stochastic analysis on path spaces.
10. B. Driver, 1995, The Lie bracket of adapted vector fields on Wiener spaces.
11. Elworthy D. Stochastic Differential Equations on Manifolds. 1982;Cambridge Univ. Press, London.
12. Elworthy D., Li X. M. A class of integration by parts formula in stochastic analysis I. Itô's Stochastic Calculus and Probability - Itô Festschrift. 1996;Springer-Verlag.
13. D. Elworthy, Y. Le Jan, X. M. Li, Concerning the geometry of stochastic differential equations and stochastic flows.
14. Emery M. Stochastic Calculus in Manifolds. 1989;Springer-Verlag, Berlin/New York.
15. O. Enchev, D. Stroock, Towards a Riemannian geometry on the path space over a Riemannian manifold, J. Funct Anal.
16. Enchev O., Stroock D. Integration by parts for pinned Brownian motion. Math. Res. Lett. 2:1995;161-169.
17. Fang S., Malliavin P. Stochastic analysis on the path space of a Riemannian manifold, I. Markovian stochastic calculus. J. Funct. Anal. 118:1993;249-274.
18. Hsu E. P. Quasiinvariance of the Wiener measure and integration by parts in the path space over a compact Riemannian manifold. J. Funct. Anal. 134:1995;417-450.
19. Hsu E. P. Flows on path space. Proc. Sympos. Pure Math. 57:1995;265-279.
20. Leandre R. Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces. J. Geom. Phys. 11:1993;517-528.
21. T. J. Lyons, Z. M. Stochastic Jacobi fields and vector fields induced by varying area on path spaces, Probab. Theory Related Fields.
22. Malliavin P. Naturality of quasi-invariance of some measures. Cruzerio A. B. Proceedings of Lisbonne Conference. 1991;Birkhäuser, Boston.
23. Malliavin P. Infinite dimensional analysis. Bull. Sci. Math. 117:1993;63-90.
24. Malliavin M.-P., Malliavin P. Integration on loop groups. I. Quasi invariant measures, Quasi invariant integration on loop groups. J. Funct. Anal. 93:1990;207-237.
25. Shigekawa I. Transformations of the Brownian motion on the Lie group. Itô K. Stochastic Analysis: Proc. of the Taniguchi International Symposium on Stochastic Analysis 1982. 1984;North-Holland.
26. Gross L. Uniqueness of ground states for Schrödinger operators over loop groups. J. Funt. Anal. 112:1993;373-441.
27. Ikeda N., Watanabe S. Stochastic Differential Equations and Diffusion Processes. 1981;North-Holland, Amsterdam.
28. Klingenberg W. Riemannian Geometry. 1982;de Gruyter, Berlin.
29. Kobayashi, Nomizu. Foundations of Differential Geometry. 1963;Wiley- Interscience, New York.
30. Kusuoka S. The nonlinear transformation of Gaussian measure on Banach space and its absolute continuity, I. J. Fac. Sci. Univ. Tokyo Sect. 1 A Math. 29:1982;567-597.
31. Milnor J. W. Morse Theory. Ann. Math. Studies. Vol. 51:1963;Princeton Univ. Press, Princeton.
32. Revuz D., Yor M. Continuous Martingales and Brownian Motion. 1991;Springer-Verlag, Berlin/New York.