Free Access
Issue
ESAIM: PS
Volume 9, June 2005
Page(s) 38 - 73
DOI https://doi.org/10.1051/ps:2005003
Published online 15 November 2005
  1. A. Araujo and E. Giné, The central limit theorem for real and Banach space valued random variables. Wiley, New York (1980).
  2. A.D. Barbour, L. Holst and S. Janson, Poisson approximation. Clarendon Press, Oxford (1992).
  3. R.E. Barlow and F. Proschan, Statistical Theory of Reliability and Life: Probability Models. Silver Spring, MD (1981).
  4. T. Birkel, On the convergence rate in the central limit theorem for associated processes. Ann. Probab. 16 (1988) 1685–1698.
  5. A.V. Bulinski, On the convergence rates in the CLT for positively and negatively dependent random fields, in Probability Theory and Mathematical Statistics, I.A. Ibragimov and A. Yu. Zaitsev Eds. Gordon and Breach Publishers, Singapore, (1996) 3–14.
  6. L.H.Y. Chen, Poisson approximation for dependent trials. Ann. Probab. 3 (1975) 534–545. [CrossRef]
  7. J.T. Cox and G. Grimmett, Central limit theorems for associated random variables and the percolation models. Ann. Probab. 12 (1984) 514–528. [CrossRef] [MathSciNet]
  8. J. Dedecker and S. Louhichi, Conditional convergence to infinitely divisible distributions with finite variance. Stochastic Proc. Appl. (To appear.)
  9. P. Doukhan and S. Louhichi, A new weak dependence condition and applications to moment inequalities. Stochastic Proc. Appl. 84 (1999) 313–342. [CrossRef] [MathSciNet]
  10. J. Esary, F. Proschan and D. Walkup, Association of random variables with applications. Ann. Math. Statist. 38 (1967) 1466–1476. [CrossRef] [MathSciNet]
  11. C. Fortuin, P. Kastelyn and J. Ginibre, Correlation inequalities on some ordered sets. Comm. Math. Phys. 22 (1971) 89–103. [CrossRef] [MathSciNet]
  12. B.V. Gnedenko and A.N. Kolmogorov, Limit distributions for sums of independent random variables. Addison-Wesley Publishing Company (1954).
  13. L. Holst and S. Janson, Poisson approximation using the Stein-Chen method and coupling: number of exceedances of Gaussian random variables. Ann. Probab. 18 (1990) 713–723. [CrossRef] [MathSciNet]
  14. T. Hsing, J. Hüsler and M.R. Leadbetter, On the Exceedance Point Process for a Stationary Sequence. Probab. Theory Related Fields 78 (1988) 97–112. [CrossRef] [MathSciNet]
  15. W.N. Hudson, H.G. Tucker and J.A Veeh, Limit distributions of sums of m-dependent Bernoulli random variables. Probab. Theory Related Fields 82 (1989) 9–17. [CrossRef] [MathSciNet]
  16. A. Jakubowski, Minimal conditions in p-stable limit theorems. Stochastic Proc. Appl. 44 (1993) 291–327. [CrossRef] [MathSciNet]
  17. A. Jakubowski, Minimal conditions in p-stable limit theorems -II. Stochastic Proc. Appl. 68 (1997) 1–20. [CrossRef]
  18. K. Joag-Dev and F. Proschan, Negative association of random variables, with applications. Ann. Statist. 11 (1982) 286–295. [CrossRef] [MathSciNet]
  19. O. Kallenberg, Random Measures. Akademie-Verlag, Berlin (1975).
  20. M. Kobus, Generalized Poisson Distributions as Limits of Sums for Arrays of Dependent Random Vectors. J. Multi. Analysis (1995) 199–244.
  21. M.R Leadbetter, G. Lindgren and H. Rootzén, Extremes and related properties of random sequences and processes. New York, Springer (1983).
  22. C.M. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, in Inequalities in Statistics and Probability, Y.L. Tong Ed. IMS Lecture Notes-Monograph Series 5 (1984) 127–140.
  23. C.M. Newman, Y. Rinott and A. Tversky, Nearest neighbors and voronoi regions in certain point processes. Adv. Appl. Prob. 15 (1983) 726–751. [CrossRef]
  24. C.M. Newman and A.L. Wright, An invariance principle for certain dependent sequences. Ann. Probab. 9 (1981) 671–675. [CrossRef] [MathSciNet]
  25. V.V. Petrov, Limit theorems of probability theory: sequences of independent random variables. Clarendon Press, Oxford (1995).
  26. L. Pitt, Positively Correlated Normal Variables are Associated. Ann. Probab. 10 (1982) 496–499. [CrossRef] [MathSciNet]
  27. E. Rio, Théorie asymptotique des processus aléatoires faiblement dépendants. Collection Mathématiques & Applications. Springer, Berlin 31 (2000).
  28. K.I. Sato, Lévy processes and infinitely divisible distributions. Cambridge studies in advanced mathematics 68 (1999).
  29. C.M. Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, in Proc. Sixth Berkeley Symp. Math. Statist. Probab. Univ. California Press 3 (1971) 583–602.