Horizontal Lift of an Infinite Dimensional Diffusion

Potential Analysis

Volumn 12, Issue 3, 2000, Pages 249-280

  Brzeźniak, Zdzisław ^a   Léandré, Remi ^b  

^a UNIVERSITY OF HULL   (United Kingdom)

^b UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

Horizontal lift; Line bundle; Loop manifold; Quantum field theory; Stochastic (Stratonovitch) differential equation

Indexed keywords

EID: 0034403791     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008622712051     Document Type: Article

References (32)

1. Amann, H.: 'Multiplication in Sobolev and Besov spaces', In Quaderni Non Linear Analysis A Tribute in Honour of Giovanni Prodi, Scuola Normale Superiore di Pisa, Pisa, 1991, 27-50.
2. Beloposkaya, Y. L. and Daletski, Y. L.: 'Stochastic equations and differential geometry', Maths. and Applications. 30, Kluwer, Dortrecht, 1990.
3. Brzeźniak, Z.: 'On stochastic convolutions in Banach spaces and applications' Stochastics Stochastics Rep., to appear.
4. Brzeźniak, Z. and Elworthy, K. D.: 'Stochastic flows of diffeomorphism'. In: Davies I. M. Truman A. Elworthy K. D. (eds.), Stochastic Analysis and applications. World Scientific (1996), 107-138.
5. Brzeźniak, Z.: Stochastic Differential Equations on Banach Manifolds: Applications to Diffusions on Loop Spaces. Preprint.
6. Brzeźniak, Z.: Manifold Structure of Besov Maps Between Manifolds, Preprint.
7. Brylinski, J. L.: 'Loop spaces, characteristic classes and geometric quantization', Progress. in Math. 107, Birkhauser, Basel, 1992.
8. Chen, K. T.: 'Iterated path integrals of differential forms and loop space homology', Ann. Maths. 97 (1973), 213-237.
9. Deligne, P.: 'Le symbole modéré', Publi. Math. IHES. 73 (1991), 147-181.
10. Driver, B.: 'A Comeron-Martin quasi-invariance formula for Brownian motion on compact manifolds', J.F.A. 110 (1992), 272-376.
11. Elworthy, K. D.: Stochastic Differential Equations on Manifolds, Lectures Notes Serie 20., L.M.S., Cambridge University Press, 1982.
12. Gawȩdzki, K., Topological actions in two-dimensional quantum field theory'. In: Gooft G't. Jaffe A. Mack G. Mitter P. K. Stora R. (eds.) Nonperturbative Quantum Field Theory NATO series 185., Plenum Press, (1988), 101-142.
13. Getzler, E., Jones, D. D. S. and Petrack, S.: 'Differential forms on loop spaces and the cyclic bar complex', topology 30 (1991), 339-371.
14. p Chen forms on loop spaces'. In: Barlow M. Bingham N. (eds.), Stochastic Analysis, Cambridge University Press, Cambridge, 1991, 104-162.
15. Jones, J. D. S. and Léandre R.: 'A stochastic approach to the Dirac operator over the free loop space'. Tr. Mat. Steklova 217, 258-287 (1997).
16. Kobayashi, S. and Nomizu, K.: Foundations of Differential Geometry, Wiley, 1963.
17. Kostant, B.: Quantization and Unitary Representations, Lectures in modern analysis and applications III, L.N.M. 170, Springer, 1970, 87-208.
18. Lang, S.: Introduction to Differentiable Manifolds, Academic Press, 1962.
19. Léandre, R.: Cohomologie de Bismut-Nualart-Pardoux et cohomoogie de Hochschild entiere, Séminaire de Probabilités XXX in honour of P. A. Meyer and J. Neveu, Azéma J. Emery M. Yor M. (eds), L.N.M. 1626, Springer, 1996, 68-100.
20. Léandre, R.: Brownian Cohomology of an Homogeneous Manifold, New trends in stochastic analysis, Elworthy K. D., Kusuoka S. Shigekawa I. (eds), World Scientific, 1997, 305-348.
21. Léandre, R.: String Structure over the Brownian Bridge. J. Math. Phys. 40(1) (1999), 454-479.
22. Léandre, R.: Hilbert Space of Spinor Fields over the Free Loop Space, Reviews in Maths. Physics. 9.2, (1997), 243-277.
23. Léandre, R.: 'Stochastic gauge transform of the string bundle', J. Geom. Phys., 26(1-2) (1998), 1-25.
24. Léandre, R.: Stochastic Wess-Zumino-Witten for the Measure of Kontsevitch, J. Geom. Phys. 21(4) (1997), 307-336.
25. Léandre, R.: Singular Integral Homology of the Stochastic Loop Space, Infin. Dimeus. Anal. Quantum Probab. Relat. Top. 1(1) (1998), 17-31.
26. Lyons, T.: Differential Equations Driven by Rough Signals. Preprint.
27. Neidhardt, A. L.: Stochastic Integrals in 2-uniformly Smooth Banach Spaces, University of Wisconsin (1978), manuscript (PhD thesis).
28. Palais, R. S.: Foundations of Global Nonlinear Analysis, Benjamin Inc., 1968.
29. Pisier, G., 'Martingales with values in uniformly convex spaces', Israel Jour. Mathematics 20 (3-4) (1976), 326-350.
30. Pressley, A.: Segal G.: Loop Groups, Oxford University Press, 1986.
31. Schwartz, L.: 'Semi-martingales a valeurs dans des espaces d'applications C∞ entre espaces vectoriels(I)', C.R.A.S., 305, Série I. (1987), 31-35.
32. Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978, 161-181.