@article{AIHPB_2004__40_2_227_0, author = {Bendikov, Alexander and Saloff-Coste, Laurent}, title = {On the sample paths of diagonal brownian motions on the infinite dimensional torus}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {40}, year = {2004}, pages = {227-254}, doi = {10.1016/j.anihpb.2003.02.001}, mrnumber = {2044817}, zbl = {1056.60029}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_2004__40_2_227_0} }
Bendikov, A.; Saloff-Coste, L. On the sample paths of diagonal brownian motions on the infinite dimensional torus. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) pp. 227-254. doi : 10.1016/j.anihpb.2003.02.001. http://gdmltest.u-ga.fr/item/AIHPB_2004__40_2_227_0/
[1] Space-homogeneous continuous Markov processes on Abelian groups and harmonic structures, Russian Math. Surveys 29 (5) (1974) 215-216. | MR 410956 | Zbl 0315.60040
,[2] Potential Theory on Infinite Dimensional Abelian Groups, De Gruyter, Berlin, 1995. | MR 1445559 | Zbl 0869.31001
,[3] Symmetric stable semigroups on the infinite dimensional torus, Expositiones Math. 13 (1995) 39-79. | MR 1339813 | Zbl 0835.31009
,[4] On- and off-diagonal heat kernel behaviors on certain infinite dimensional local Dirichlet spaces, Amer. J. Math. 122 (2000) 1205-1263. | MR 1797661 | Zbl 0969.31008
, ,[5] Central Gaussian semigroups of measures with continuous density, J. Funct. Anal. 186 (2001) 206-268. | MR 1863298 | Zbl 0989.43002
, ,[6] A. Bendikov, L. Saloff-Coste, Central Gaussian convolution semigroups on compact groups: a survey, Infinite Dimensional Analysis, Quantum Probability and Related Topics, in press. | MR 2030215 | Zbl 1043.60068
[7] On the sample paths of Brownian motions on compact infinite dimensional groups, Ann. Probab. 31 (2003) 1464-1493. | MR 1989440 | Zbl 1043.60064
, ,[8] A. Bendikov, L. Saloff-Coste, On the sample paths of subelliptic diffusions on manifolds, in preparation.
[9] Potential theory on the infinite dimensional torus, Inventiones Math. 32 (1976) 49-100. | MR 402093 | Zbl 0371.31007
,[10] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation. Encyclopedia of Mathematics and its Applications, Cambridge University Press. | MR 898871 | Zbl 0617.26001
[11] Formes de Dirichlet et estimations structurelles dans les milieux discontinus, C. R. Acad. Sci. Paris 313 (1991) 593-598. | MR 1133491 | Zbl 0760.49004
, ,[12] Markov Processes and Potential Theory, Academic Press, 1968. | MR 264757 | Zbl 0169.49204
, ,[13] Heat Kernels and Spectral Theory, Cambridge University Press, 1989. | MR 990239 | Zbl 0699.35006
,[14] Some problems on random walk in space, in: Second Berkeley Symp., University of California Press, 1951, pp. 353-367. | MR 47272 | Zbl 0044.14001
, ,[15] Dirichlet Forms and Symmetric Markov Processes, De Gruyter, 1994. | MR 1303354 | Zbl 0838.31001
, , ,[16] Escape rate of Brownian motion on Riemannian manifolds, Appl. Anal. 71 (1999) 63-89. | MR 1690091 | Zbl 1020.58024
,[17] Probability Measures on Locally Compact Groups, Ergeb. Math. Grenzgeb., vol. 94, Springer, Berlin, 1977. | MR 501241 | Zbl 0376.60002
,[18] Diffusion Processes and their Sample Paths, Springer, 1974. | MR 345224 | Zbl 0127.09503
, ,[19] Continuous Martingales and Brownian Motion, Springer, 1994. | MR 1303781 | Zbl 0804.60001
, ,[20] On the geometry defined by Dirichlet forms, in: , (Eds.), Seminar on Stochastic Processes, Random Fields and Applications, Ascona, Progress in Probability, vol. 36, Birkhäuser, 1995, pp. 231-242. | MR 1360279 | Zbl 0834.58039
,[21] Sharp estimates for capacities and applications to symmetric diffusions, Probab. Theory Related Fields 103 (1995) 73-89. | MR 1347171 | Zbl 0828.60062
,