On the sample paths of diagonal brownian motions on the infinite dimensional torus

Bendikov, A.; Saloff-Coste, L.

doi:10.1016/j.anihpb.2003.02.001

Bendikov, A. ; Saloff-Coste, L.

Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 2, pp. 227-254

MR Zbl

DOI : 10.1016/j.anihpb.2003.02.001

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     author = {Bendikov, A. and Saloff-Coste, L.},
     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},
     pages = {227--254},
     year = {2004},
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     number = {2},
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     mrnumber = {2044817},
     zbl = {1056.60029},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2003.02.001/}
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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) no. 2, pp. 227-254. doi: 10.1016/j.anihpb.2003.02.001

Bibliographie
Cité par

[1] A. Bendikov, Space-homogeneous continuous Markov processes on Abelian groups and harmonic structures, Russian Math. Surveys 29 (5) (1974) 215-216. | Zbl | MR

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

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

[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. | Zbl | MR

[5] A. Bendikov, L. Saloff-Coste, Central Gaussian semigroups of measures with continuous density, J. Funct. Anal. 186 (2001) 206-268. | Zbl | MR

[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. | Zbl | MR

[7] A. Bendikov, L. Saloff-Coste, On the sample paths of Brownian motions on compact infinite dimensional groups, Ann. Probab. 31 (2003) 1464-1493. | Zbl | MR

[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. | Zbl | MR

[10] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation. Encyclopedia of Mathematics and its Applications, Cambridge University Press. | Zbl | MR

[11] M. Biroli, U. Mosco, Formes de Dirichlet et estimations structurelles dans les milieux discontinus, C. R. Acad. Sci. Paris 313 (1991) 593-598. | Zbl | MR

[12] R. Blumenthal, R. Getoor, Markov Processes and Potential Theory, Academic Press, 1968. | Zbl | MR

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

[14] A. Dvoretzky, P. Erdös, Some problems on random walk in space, in: Second Berkeley Symp., University of California Press, 1951, pp. 353-367. | Zbl | MR

[15] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, De Gruyter, 1994. | Zbl | MR

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

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

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

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

[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. | Zbl | MR

[21] K.-T. Sturm, Sharp estimates for capacities and applications to symmetric diffusions, Probab. Theory Related Fields 103 (1995) 73-89. | Zbl | MR

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