Vector fields on mapping spaces and related dirichlet forms and diffusions

Osaka Journal of Mathematics

Volumn 34, Issue 3, 1997, Pages 629-651

  Elworthy, K David ^a   Ma, Zhi Ming ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041105036     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. S. Albeverio, S. Leandre and M. Röckner: Construction of a rotational invariant diffusion on the free loop space, C.R.A.S. 316 (1993), 287-292.
2. S. Albeverio, Z.M. Ma and M. Röckner: Quasi-regular Dirichlet forms and Markov processes, J. Funct. Anal. 111 (1992), 118-154.
3. C.J. Atkin: Bounded complete Finsler structures 1, Studia Math. LXII (1978), 219-228.
4. V.I. Bogachev: Differential measures and Malliavin calculus, Preprints di Mathematica, 16 (1995), ScuAla Normale Superiore, Pisa.
5. C. Caratheodory: Untersuchungen über die Grundlagen der Thermodynamik, Math. Ann. 67 (1909), 355-386.
6. B. Driver: A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, J. Funct. Anal. 100 (1992), 272-377.
7. B. Driver: The Lie bracket of adapted vector fields on Wiener spaces, Preprint, 1995.
8. B. Driver and M. Röckner: Construction of diffusions on path and loop spaces of compact Riemannian manifold, C.R.A.S. 315 (1992), 603-608.
9. H. Eliasson: Geometry of manifolds of map, J. Diff. Geom. 1 (1966), 169-194.
10. K.D. El worthy: Embedding, isotopy and stability of Banach manifolds, Compositio Mathematica, 24 (1972), 175-225.
11. K.D. Elworthy: Differential invariants of measures on Banach spaces, in Vector Spaces measures and Applications I, eds R.M. Aron & S. Dineen, Lecture Notes in Maths, 644 (1978), 159-187.
12. K.D. Elworthy: Stochastic differential equations on manifolds, LMS Lecture Note Series 70, Combridge Uni. Press, London, 1982.
13. K.D. Elworthy and X.M. Li: A class of integration by parts formulae in stochastic analysis, Ito's stochastic calculus and probability theory, eds N. Ikeda et al. Springer-Verlag, 1996, 15-30.
14. S. Fang: Stochastic anticipative integrals on a Riemannian Manifold, J. Funct. Anal. 131 (1995), 228-253.
15. M. Fukushima: Dirichlet forms and Markov processes, Amsterdam-Oxford-New York, North Holland, 1980.
16. M. Fukushima, Y. Oshima and M. Takeda: Dirichlet forms and symmetric Markov processes, Walter de Gruyter, Berlin, 1994.
17. K. Ito: Foundations of stochastic differential equations in infinite dimensional Hilbert spaces, CBMS-NSF Regional Conference Series in Applied Mathematics, 47, S.I.A.M., 1984.
18. p Chen forms in Stochastic Analysis, in Proc. of Durham Symposium 1990 M. Barlow and N. Bingham eds, LMS Lectures Note Series, 167, Cambridge University Press, London, (1991), 104-162.
19. J.L. Kelly: General Topology, Von Nostrand, 1955.
20. N. Krikorian: Differentiable structures on function spaces, Trans Amer. Math. Soc. 17 (1972), 67-82.
21. Z.M. Ma, L. Overbeck and M. Röckner: Markov processes associated with semi-Dirichlet forms, Osaka J. Math. 32 (1995), 97-119.
22. Z.M. Ma and M. Röckner: Introduction to the Theory of (non-symmetric) Dirichlet Forms, Springer, Berlin, 1992.
23. Z.M. Ma and M. Röckner: Markov processes associated with positivity preserving coercive forms, Canadian J. Math. 47 (1995), 817-840.
24. R.S. Palais: Lusternik-Schnirelman theory on Banach manifolds, Topology, 5 (1966), 115-132.
25. J.P. Penot: Varietés differentiables d'applications et de chemins. C.R. Acad. Sci Paris, Ser. A-B264 (1967), A1066-A1068.
26. M. Röckner and M. Schmuland: Quasi-regular Dirichlet forms, Examples and counterexamples, Canadian J. Math. 47 (1995), 165-200.
27. W. Stannat: The theory of generalized Dirichlet forms and its applications in analysis and stochastics, Ph.D. Thesis, Bielefeld, 1996.