Free Access
Volume 5, 2001
Page(s) 77 - 104
Published online 15 August 2002
  1. P. Hall and C.C. Heyde, Martingale Limit Theory and its Applications. Academic Press, New York (1980).
  2. K.S. Alexander and R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance. Ann. Probab. 14 (1986) 582-597. [CrossRef] [MathSciNet]
  3. K. Azuma, Weighted sums of certain dependent random fields. Tôhoku Math. J. (2) 19 (1967) 357-367. [CrossRef]
  4. 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. [CrossRef] [MathSciNet]
  5. A.K. Basu and C.C.Y. Dorea, On functional central limit theorem for stationary martingale random fields. Acta Math. Hungar. 33 (1979) 307-316. [CrossRef]
  6. P.J. Bickel and M.J. Wichura, Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42 (1971) 1656-1670. [CrossRef] [MathSciNet]
  7. R. Bradley, A caution on mixing conditions for random fields. Statist. Probab. Lett. 8 (1989) 489-491. [CrossRef] [MathSciNet]
  8. D. Chen, A uniform central limit theorem for nonuniform Φ-mixing random fields. Ann. Probab. 19 (1991) 636-649. [CrossRef] [MathSciNet]
  9. J. Dedecker, A central limit theorem for stationary random fields. Probab. Theory Related Fields 110 (1998) 397-426. [CrossRef] [MathSciNet]
  10. J. Dedecker and E. Rio, On the functional central limit theorem for stationary processes. Ann. Inst. H. Poincaré Probab. Statist. 36 (2000) 1-34. [CrossRef] [MathSciNet]
  11. R.L. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularity. Theory Probab. Appl. 13 (1968) 197-224. [CrossRef]
  12. R.L. Dobrushin and S. Shlosman, constructive criterion for the uniqueness of Gibbs fields, Statistical physics and dynamical systems. Birkhauser (1985) 347-370.
  13. P. Doukhan, Mixing: Properties and Examples. Springer, Berlin, Lecture Notes in Statist. 85 (1994).
  14. P. Doukhan, J. León and F. Portal, Vitesse de convergence dans le théorème central limite pour des variables aléatoires mélangeantes à valeurs dans un espace de Hilbert. C. R. Acad. Sci. Paris Sér. I Math. 298 (1984) 305-308.
  15. R.M. Dudley, Sample functions of the Gaussian process. Ann. Probab. 1 (1973) 66-103. [CrossRef]
  16. C.M. Goldie and 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. [CrossRef] [MathSciNet]
  17. C.M. Goldie and G.J. Morrow, Central limit questions for random fields, Dependence in probability and statistics. Progr. Probab. Statist. 11 (1986) 275-289.
  18. Y. Higuchi, Coexistence of infinite (*)-clusters II. Ising percolation in two dimensions. Probab. Theory Related Fields 97 (1993) 1-33. [CrossRef] [MathSciNet]
  19. E. Laroche, Hypercontractivité pour des systèmes de spins de portée infinie. Probab. Theory Related Fields 101 (1995) 89-132. [CrossRef] [MathSciNet]
  20. M. Ledoux and M. Talagrand, Probability in Banach Spaces. Springer, New York (1991).
  21. P. Lezaud, Chernoff-type bound for finite Markov chains. Ann. Appl. Probab. 8 (1998) 849-867. [CrossRef] [MathSciNet]
  22. F. Martinelli and E. Olivieri, Approach to Equilibrium of Glauber Dynamics in the One Phase Region. I. The Attractive Case. Comm. Math. Phys. 161 (1994) 447-486. [CrossRef] [MathSciNet]
  23. M. Peligrad, A note on two measures of dependence and mixing sequences. Adv. in Appl. Probab. 15 (1983) 461-464. [CrossRef] [MathSciNet]
  24. G. Perera, Geometry of Formula and the central limit theorem for weakly dependent random fields. J. Theoret. Probab. 10 (1997).
  25. I.F. Pinelis, Optimum bounds for the distribution of martingales in Banach spaces. Ann. Probab. 22 (1994) 1679-1706. [CrossRef] [MathSciNet]
  26. E. Rio, Covariance inequalities for strongly mixing processes. Ann. Inst. H. Poincaré 29 (1993) 587-597.
  27. E. Rio, Théorèmes limites pour les suites de variables aléatoires faiblement dépendantes. Springer, Berlin, Collect. Math. Apll. 31 (2000).
  28. P.M. Samson, Inégalités de concentration de la mesure pour des chaînes de Markov et des processus Φ-mélangeants, Thèse de doctorat de l'université Paul Sabatier (1998).
  29. R.H. Schonmann and S.B. Shlosman, Complete Analyticity for 2D Ising Completed. Comm. Math. Phys. 170 (1995) 453-482. [CrossRef] [MathSciNet]
  30. R.J. Serfling, Contributions to Central Limit Theory For Dependent Variables. Ann. Math. Statist. 39 (1968) 1158-1175. [CrossRef] [MathSciNet]

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