On the sample paths of diagonal brownian motions on the infinite dimensional torus
Annales de l'I.H.P. Probabilités et statistiques, Volume 40 (2004) no. 2, p. 227-254
@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},
     publisher = {Elsevier},
     volume = {40},
     number = {2},
     year = {2004},
     pages = {227-254},
     doi = {10.1016/j.anihpb.2003.02.001},
     zbl = {1056.60029},
     mrnumber = {2044817},
     language = {en},
     url = {http://www.numdam.org/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, Volume 40 (2004) no. 2, pp. 227-254. doi : 10.1016/j.anihpb.2003.02.001. http://www.numdam.org/item/AIHPB_2004__40_2_227_0/

[1] A. Bendikov, 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] A. Bendikov, Potential Theory on Infinite Dimensional Abelian Groups, De Gruyter, Berlin, 1995. | MR 1445559 | Zbl 0869.31001

[3] A. Bendikov, Symmetric stable semigroups on the infinite dimensional torus, Expositiones Math. 13 (1995) 39-79. | MR 1339813 | Zbl 0835.31009

[4] A. Bendikov, L. Saloff-Coste, 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] A. Bendikov, L. Saloff-Coste, 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] A. Bendikov, L. Saloff-Coste, 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] C. Berg, 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] M. Biroli, U. Mosco, 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] R. Blumenthal, R. Getoor, Markov Processes and Potential Theory, Academic Press, 1968. | MR 264757 | Zbl 0169.49204

[13] E.B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, 1989. | MR 990239 | Zbl 0699.35006

[14] A. Dvoretzky, P. Erdös, 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] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, De Gruyter, 1994. | MR 1303354 | Zbl 0838.31001

[16] A. Grigor'Yan, Escape rate of Brownian motion on Riemannian manifolds, Appl. Anal. 71 (1999) 63-89. | MR 1690091 | Zbl 1020.58024

[17] H. Heyer, Probability Measures on Locally Compact Groups, Ergeb. Math. Grenzgeb., vol. 94, Springer, Berlin, 1977. | MR 501241 | Zbl 0376.60002

[18] K. Ito, P. Mckean, Diffusion Processes and their Sample Paths, Springer, 1974. | MR 345224 | Zbl 0127.09503

[19] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, 1994. | MR 1303781 | Zbl 0804.60001

[20] K.-T. Sturm, On the geometry defined by Dirichlet forms, in: Bolthausen E., (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] K.-T. Sturm, Sharp estimates for capacities and applications to symmetric diffusions, Probab. Theory Related Fields 103 (1995) 73-89. | MR 1347171 | Zbl 0828.60062