Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels
El Machkouri, Mohamed ; Volný, Dalibor
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003), p. 325-337 / Harvested from Numdam
@article{AIHPB_2003__39_2_325_0,
     author = {El Machkouri, Mohamed and Voln\'y, Dalibor},
     title = {Contre-exemple dans le th\'eor\`eme central limite fonctionnel pour les champs al\'eatoires r\'eels},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {39},
     year = {2003},
     pages = {325-337},
     doi = {10.1016/S0246-0203(02)00011-0},
     mrnumber = {1962780},
     zbl = {1014.60055},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_2003__39_2_325_0}
}
El Machkouri, Mohamed; Volný, Dalibor. Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) pp. 325-337. doi : 10.1016/S0246-0203(02)00011-0. http://gdmltest.u-ga.fr/item/AIHPB_2003__39_2_325_0/

[1] K.S. Alexander, R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance, Ann. Probab. 14 (1986) 582-597. | MR 832025 | Zbl 0595.60027

[2] R.F. Bass, Law of the iterated logarithm for set-indexed partial sum processes with finite variance, Z. Wahrsch. Verw. Gebiete 70 (1985) 591-608. | MR 807339 | Zbl 0575.60034

[3] A.K. Basu, C.C.Y. Dorea, On functional central limit theorem for stationary martingale random fields, Acta. Math. Hung. 33 (1979) 307-316. | MR 542479 | Zbl 0431.60037

[4] D. Chen, A uniform central limit theorem for nonuniform φ-mixing random fields, Ann. Probab. 19 (1991) 636-649. | Zbl 0735.60034

[5] J.P. Conze, Entropie d'un groupe abélien de transformations, Z. Wahrsch. Verw. Geb. 25 (1972) 11-30. | MR 335754 | Zbl 0261.28015

[6] J. Dedecker, Principes d'invariances pour les champs aléatoires stationnaires, PhD thesis, Université Paris XI Orsay, 1998.

[7] J. Dedecker, Exponential inequalities and functional central limit theorems for random fields, ESAIM, 2001, to appear. | Numdam | MR 1875665 | Zbl 1003.60033

[8] R.L. Dobrushin, B.S. Nahapetian, Strong convexity of pressure for lattice systems of classical statistical physics, Teoret. Mat. Fiz. 20 (1974) 223-234. | MR 468967 | Zbl 0311.60063

[9] M.D. Donsker, An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc. 6 (1951) 1-12. | MR 40613 | Zbl 0042.37602

[10] R.M. Dudley, Sample functions of the Gaussian process, Ann. Probab. 1 (1973) 66-103. | MR 346884 | Zbl 0261.60033

[11] C.M. Goldie, P.E. Greenwood, Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes, Ann. Probab. 14 (1986) 817-839. | MR 841586 | Zbl 0604.60032

[12] Y. Katznelson, B. Weiss, Commuting measure-preserving transformations, Israel J. Math. 12 (1972) 161-173. | MR 316680 | Zbl 0239.28014

[13] J. Kuelbs, The invariance principle for a lattice of random variables, Ann. Math. Statist. 39 (1968) 382-389. | MR 226713 | Zbl 0164.46401

[14] M. El Machkouri, Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields, Stoch. Proc. Appl. 120 (2002) 285-299. | Zbl 1075.60506

[15] B. Nahapetian, A.N. Petrosian, Martingale-difference Gibbs random fields and central limit theorem, Ann. Acad. Sci. Fenn., Series A-I Math. 17 (1992) 105-110. | MR 1162153 | Zbl 0789.60043

[16] D.S. Ornstein, B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, Journal d'Analyse Mathématique 48 (1987) 1-141. | MR 910005 | Zbl 0637.28015

[17] D. Pollard, Empirical Processes: Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics, IMS-ASA, Hayward-Alexandria, 1990. | MR 1089429 | Zbl 0741.60001

[18] R. Pyke, A uniform central limit theorem for partial-sum processes indexed by sets, London Math. Soc. Lect. Notes Series 79 (1983) 219-240. | MR 696030 | Zbl 0497.60030

[19] M.J. Wichura, Inequalities with applications to the weak convergence of random processes with multi-dimensional time parameters, Ann. Math. Statist. 40 (1969) 681-687. | MR 246359 | Zbl 0214.17701