On the sample paths of Brownian motions on compact infinite dimensional groups

Annals of Probability

Volumn 31, Issue 3, 2003, Pages 1464-1493

  Bendikov, Alexander ^a   Saloff Coste, Laurent ^a  

^a Malott Hall ^*  (United States)

Author keywords

Gaussian convolution semigroups; Invariant diffusions; Path regularity

Indexed keywords

EID: 0037696886     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1055425787     Document Type: Article

References (30)

1. BENDIKOV, A. (1976). On harmonic functions for a category of Markov processes and projective limits in it. Russian Math. Surv. 31 209-210.
2. BENDIKOV, A. (1995). Potential Theory on Infinite-Dimensional Abelian Groups. de Gruyter, Berlin.
3. BENDIKOV, A. (1995). Symmetric stable semigroups on the infinite-dimensional torus. Exposiones Math. 13 39-79.
4. BENDIKOV, A. and SALOFF-COSTE, L. (1997). Elliptic diffusions on infinite products. J. Reine Angew. Math. 493 171-220.
5. BENDIKOV, A. and SALOFF-COSTE, L. (1999). Potential theory on infinite products and groups. Potential Anal. 11 325-358.
6. BENDIKOV, A. and SALOFF-COSTE, L. (2000). On- and off-diagonal heat kernel behaviors on certain infinite-dimensional local Dirichlet spaces. Amer. J. Math. 122 1205-1263.
7. BENDIKOV, A. and SALOFF-COSTE, L. (2001). Central Gaussian semigroups of measures with continuous density. J. Funct. Anal. 186 206-268.
8. BENDIKOV, A. and SALOFF-COSTE, L. (2001). On the absolute continuity of Gaussian measures on locally compact groups. J. Theoret. Probab. 14 887-898.
9. BENDIKOV, A. and SALOFF-COSTE, L. (2000). Gaussian semigroups of measures on locally compact locally connected groups. Preprint.
10. BENDIKOV, A. and SALOFF-COSTE, L. (2002). Some properties of the paths of subelliptic diffusions. Unpublished manuscript.
11. BENDIKOV, A. and SALOFF-COSTE, L. (2002). On the sample paths of Brownian motions on double-struck T∞, Preprint.
12. BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L. (1989). Regular Variation. Encyclopedia of Mathematics and Its Applications. Cambridge Univ. Press.
13. BLUMENTHAL, R. and GETOOR, R. (1968). Markov Processes and Potential Theory. Academic Press, New York.
14. BRUHAT, F. (1961). Distributions sur un groupe localement compact et application à l'étude des représentations des groupes p-adiques. Bull. Soc. Math. France 89 43-75.
15. DAVIES, E. B. (1989). Heat Kernels and Spectral Theory. Cambridge Univ. Press.
16. DVORETZKY, A. and ERDÖS, P. (1951). Some problems on random walk in space. Proc. Second Berkeley Symp. Math. Statist. Probab. 353-367. Univ. California Press, Berkeley.
17. FUKUSHIMA M., OSHIMA Y. and TAKEDA, M. (1994). Dirichlet Forms and Symmetric Markov Processes. de Gruyter, Berlin.
18. GRIGOR'YAN, A. (1999). Escape rate of Brownian motion on Riemannian manifolds. Appl. Anal. 71 63-89.
19. GRIGOR'VAN, A. and KELBERT, M. (1998). Range of fluctuation of Brownian on a complete Riemannian manifold. Ann. Probab. 26 78-111.
20. HEYER, H. (1977). Probability Measures on Locally Compact Groups. Springer, Berlin.
21. HOFMANN, K. and MORRIS, S. (1998). The Structure of Compact Groups. de Gruyter, Berlin.
22. HÖRMANDER, L. (1967). Hypoelliptic second order differential equations. Acta Math. 119 147-171.
23. HUNT, G. A. (1956). Semi-groups of measures on Lie groups. Trans. Amer. Math. Soc. 81 264-293.
24. ITÔ, K. and McKEAN, P. (1974). Diffusion Processes and Their Sample Paths. Springer, Berlin.
25. KUELBS, J. and LEPAGE, R. (1973). The law of iterated logarithm for Brownian motion on a Banach space. Trans. Amer. Math. Soc. 185 253-264.
26. LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces. Springer, Berlin.
27. REVUZ, D. and YOR, M. (1994). Continuous Martingales and Brownian Motion, 2nd ed. Springer, Berlin.
28. SIEBERT, E. (1982). Absolute continuity, singularity and supports of Gaussian semigroups on a Lie group. Monatshefte für Math. 93 239-253.
29. STURM, K.-T. (1995). On the geometry defined by Dirichlet forms. In Seminar on Stochastic Processes, Random Fields and Applications (E. Bolthausen, M. Dozzi and F. Russo, eds.) 231-242. Birkhäuser, Boston.
30. VAROPOULOS, N., SALOFF-COSTE, L. and COULHON, T. (1993). Analysis and Geometry on Groups. Cambridge Univ. Press.