Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels

Mohamed El Machkouri; Dalibor Volný

Annales de l'I.H.P. Probabilités et statistiques (2003)

  • Volume: 39, Issue: 2, page 325-337
  • ISSN: 0246-0203

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El Machkouri, Mohamed, and Volný, Dalibor. "Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels." Annales de l'I.H.P. Probabilités et statistiques 39.2 (2003): 325-337. <http://eudml.org/doc/77765>.

@article{ElMachkouri2003,
author = {El Machkouri, Mohamed, Volný, Dalibor},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {metric entropy; invariance principle; ergodic dynamical system; positive entropy; entropy condition with inclusion; stationary martingale-difference random field; functional central limit theorem},
language = {fre},
number = {2},
pages = {325-337},
publisher = {Elsevier},
title = {Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels},
url = {http://eudml.org/doc/77765},
volume = {39},
year = {2003},
}

TY - JOUR
AU - El Machkouri, Mohamed
AU - Volný, Dalibor
TI - Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 2
SP - 325
EP - 337
LA - fre
KW - metric entropy; invariance principle; ergodic dynamical system; positive entropy; entropy condition with inclusion; stationary martingale-difference random field; functional central limit theorem
UR - http://eudml.org/doc/77765
ER -

References

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  1. [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. Zbl0595.60027MR832025
  2. [2] R.F. Bass, Law of the iterated logarithm for set-indexed partial sum processes with finite variance, Z. Wahrsch. Verw. Gebiete70 (1985) 591-608. Zbl0575.60034MR807339
  3. [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. Zbl0431.60037MR542479
  4. [4] D. Chen, A uniform central limit theorem for nonuniform φ-mixing random fields, Ann. Probab.19 (1991) 636-649. Zbl0735.60034
  5. [5] J.P. Conze, Entropie d'un groupe abélien de transformations, Z. Wahrsch. Verw. Geb.25 (1972) 11-30. Zbl0261.28015MR335754
  6. [6] J. Dedecker, Principes d'invariances pour les champs aléatoires stationnaires, PhD thesis, Université Paris XI Orsay, 1998. 
  7. [7] J. Dedecker, Exponential inequalities and functional central limit theorems for random fields, ESAIM, 2001, to appear. Zbl1003.60033MR1875665
  8. [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. Zbl0311.60063MR468967
  9. [9] M.D. Donsker, An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc.6 (1951) 1-12. Zbl0042.37602MR40613
  10. [10] R.M. Dudley, Sample functions of the Gaussian process, Ann. Probab.1 (1973) 66-103. Zbl0261.60033MR346884
  11. [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. Zbl0604.60032MR841586
  12. [12] Y. Katznelson, B. Weiss, Commuting measure-preserving transformations, Israel J. Math.12 (1972) 161-173. Zbl0239.28014MR316680
  13. [13] J. Kuelbs, The invariance principle for a lattice of random variables, Ann. Math. Statist.39 (1968) 382-389. Zbl0164.46401MR226713
  14. [14] M. El Machkouri, Kahane–Khintchine inequalities and functional central limit theorem for stationary random fields, Stoch. Proc. Appl.120 (2002) 285-299. Zbl1075.60506
  15. [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. Zbl0789.60043MR1162153
  16. [16] D.S. Ornstein, B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, Journal d'Analyse Mathématique48 (1987) 1-141. Zbl0637.28015MR910005
  17. [17] D. Pollard, Empirical Processes: Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics, IMS-ASA, Hayward-Alexandria, 1990. Zbl0741.60001MR1089429
  18. [18] R. Pyke, A uniform central limit theorem for partial-sum processes indexed by sets, London Math. Soc. Lect. Notes Series79 (1983) 219-240. Zbl0497.60030MR696030
  19. [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. Zbl0214.17701MR246359

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