Sur l'existence des suites de variables aléatoires s à s indépendantes échangeables ou stationnaires

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1. [1] D.J. Aldous, Exchangeability and related topics, Springer Lecture Notes in Math., Vol. 1117, 1983, pp. 1-198. Zbl0562.60042MR883646
2. [2] C.B. Bell, Maximal independent stochastic processes, Ann. Math. Statist., Vol. 32, 1961, pp. 704-708. Zbl0101.11203MR126866
3. [3] S.N. Bernstein, Théorie des probabilités, en Russe, Gostechizdat, Moscou-Leningrad, 4e éd., 1946. Zbl0063.00337
4. [3 bis] P. Billingsley, Ergodic Theory and Information, Wiley Series in Probability and Mathematical Statistics, 1965. Zbl0141.16702MR192027
5. [4] R.C. Bradley, A stationary, pairwise independent, absolutely regular sequence for which the central limit theorem fails, Probab. Th. Rel. Fields, Vol. 81, 1989, pp. 1-10. Zbl0649.60017MR981565
6. [5] S. Csörgö, K. Tandori et V. Totik, On the strong law of large numbers for pairwise independent random variables, Ann. Math. Hung., Vol. 42, 1983, p. 319-330. Zbl0534.60028MR722846
7. [6] P.H. Diananda, The central limit theorem for m-dependent variables, Proc. Cambridge Philos. Soc., Vol. 51, 1955, p. 92-95. Zbl0064.13104MR67396
8. [7] Y. Derriennic, Une lettre, Janvier 1991. 
9. [8] Y. Derriennic et A. Klopotowski, Cinq variables aléatoires binaires stationnaires deux à deux indépendantes, Prépubl. Institut Galilée, Université Paris XIII, Novembre 1991, p. 1-38. 
10. [9] Y. Derriennic et A. Klopotowski, Sur les hypothèses constructibles concernant des suites de variables aléatoires binaires, Idem, Décembre 1991, p. 1-10. 
11. [10] N. Etemadi, An elementary proof of the strong law of large numbers, Z. Wahrsch. verw. Gebiete, Vol. 55, 1981, p. 119-122. Zbl0438.60027MR606010
12. [11] S. Geisser et N. Mantel, Pairwise independence of jointly dependent variables, Ann. Math. Statist., Vol. 32, 1962, pp. 290-291. Zbl0102.35802MR137188
13. [12] C.P. Han, Dependence of random variables, The Amer. Statist., Vol. 25, 1971, p. 35. Zbl0493.33006
14. [13] S. Janson, Some pairwise independent sequences for which the central limit theorem fails, Stochastics, Vol. 23, 1988, pp. 439-448. Zbl0645.60027MR943814
15. [14] A. Joffe, On a sequence of almost deterministic pairwise independent random variables, Proc. Amer. Math. Soc., Vol. 29, 1971, pp. 381-382. Zbl0217.21102MR279857
16. [15] A. Joffe, On a set of almost deterministic k-independent random variables, Ann. of Prob., Vol. 2, 1974, pp. 161-162. Zbl0276.60005MR356150
17. [16] J.F.C. Kingman, Uses of exchangeability, Ann. of Prob., Vol. 6, 1978, pp. 183-197. Zbl0374.60064MR494344
18. [17] H.O. Lancaster, Pairwise statistical independence, Ann. Math. Statist., Vol. 36, 1965, pp. 1313-1317. Zbl0131.18105MR176507
19. [18] P. Lévy, Exemple de processus pseudo-Markoviens, C. R. Acad. Sci. Paris, Vol. 228, 1949, pp. 2004-2006. Zbl0041.25201MR31218
20. [19] G.L. O'Brien, Pairwise independent random variables, Ann. of Prob., Vol. 8, 1980, pp. 170-175. Zbl0426.60011MR556424
21. [20] E.J.G. Pitman et E.J. Williams, Cauchy - distributed functions of Cauchy variates, Ann. Math. Statist., Vol. 38, 1967, pp. 916-918. Zbl0201.51104MR210166
22. [21] J.B. Robertson, Independence and Fair Coin-Tossing, Math. Scientist, Vol. 10, 1985, pp. 109-117. Zbl0583.60031MR832126
23. [22] J.B. Robertson et J.M. Womack, A pairwise independent stationary stochastic process, Statistics and Probability Letters, Vol. 3, 1985, pp. 195-199. Zbl0569.60041MR801689
24. [23] M. Rosenblatt et D. Slepian, Nth order Markov chain with every N variables independent, J. SIAM, Vol. 10, 1962, pp. 537-549. Zbl0154.43103MR150824
25. [24] J.M. Stoyanov, Counterexamples in probability, John Wiley & Sons, 1987. Zbl0629.60001

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