Sur l'existence des suites de variables aléatoires s à s indépendantes échangeables ou stationnaires
Bretagnolle, Jean ; Klopotowski, Andrzej
Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995), p. 325-350 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1995-01-01
@article{AIHPB_1995__31_2_325_0,
     author = {Bretagnolle, Jean and Klopotowski, Andrzej},
     title = {Sur l'existence des suites de variables al\'eatoires s \`a s ind\'ependantes \'echangeables ou stationnaires},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {31},
     year = {1995},
     pages = {325-350},
     mrnumber = {1324811},
     zbl = {0819.60035},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1995__31_2_325_0}
}

Bretagnolle, Jean; Klopotowski, Andrzej. Sur l'existence des suites de variables aléatoires s à s indépendantes échangeables ou stationnaires. Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) pp. 325-350. http://gdmltest.u-ga.fr/item/AIHPB_1995__31_2_325_0/

[1] D.J. Aldous, Exchangeability and related topics, Springer Lecture Notes in Math., Vol. 1117, 1983, pp. 1-198. | MR 883646 | Zbl 0562.60042

[2] C.B. Bell, Maximal independent stochastic processes, Ann. Math. Statist., Vol. 32, 1961, pp. 704-708. | MR 126866 | Zbl 0101.11203

[3] S.N. Bernstein, Théorie des probabilités, en Russe, Gostechizdat, Moscou-Leningrad, 4e éd., 1946.

[3 bis] P. Billingsley, Ergodic Theory and Information, Wiley Series in Probability and Mathematical Statistics, 1965. | MR 192027 | Zbl 0141.16702

[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. | MR 981565 | Zbl 0649.60017

[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. | MR 722846 | Zbl 0534.60028

[6] P.H. Diananda, The central limit theorem for m-dependent variables, Proc. Cambridge Philos. Soc., Vol. 51, 1955, p. 92-95. | MR 67396 | Zbl 0064.13104

[7] Y. Derriennic, Une lettre, Janvier 1991.

[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.

[9] Y. Derriennic et A. Klopotowski, Sur les hypothèses constructibles concernant des suites de variables aléatoires binaires, Idem, Décembre 1991, p. 1-10.

[10] N. Etemadi, An elementary proof of the strong law of large numbers, Z. Wahrsch. verw. Gebiete, Vol. 55, 1981, p. 119-122. | MR 606010 | Zbl 0438.60027

[11] S. Geisser et N. Mantel, Pairwise independence of jointly dependent variables, Ann. Math. Statist., Vol. 32, 1962, pp. 290-291. | MR 137188 | Zbl 0102.35802

[12] C.P. Han, Dependence of random variables, The Amer. Statist., Vol. 25, 1971, p. 35. | Zbl 0493.33006

[13] S. Janson, Some pairwise independent sequences for which the central limit theorem fails, Stochastics, Vol. 23, 1988, pp. 439-448. | MR 943814 | Zbl 0645.60027

[14] A. Joffe, On a sequence of almost deterministic pairwise independent random variables, Proc. Amer. Math. Soc., Vol. 29, 1971, pp. 381-382. | MR 279857 | Zbl 0217.21102

[15] A. Joffe, On a set of almost deterministic k-independent random variables, Ann. of Prob., Vol. 2, 1974, pp. 161-162. | MR 356150 | Zbl 0276.60005

[16] J.F.C. Kingman, Uses of exchangeability, Ann. of Prob., Vol. 6, 1978, pp. 183-197. | MR 494344 | Zbl 0374.60064

[17] H.O. Lancaster, Pairwise statistical independence, Ann. Math. Statist., Vol. 36, 1965, pp. 1313-1317. | MR 176507 | Zbl 0131.18105

[18] P. Lévy, Exemple de processus pseudo-Markoviens, C. R. Acad. Sci. Paris, Vol. 228, 1949, pp. 2004-2006. | MR 31218 | Zbl 0041.25201

[19] G.L. O'Brien, Pairwise independent random variables, Ann. of Prob., Vol. 8, 1980, pp. 170-175. | MR 556424 | Zbl 0426.60011

[20] E.J.G. Pitman et E.J. Williams, Cauchy - distributed functions of Cauchy variates, Ann. Math. Statist., Vol. 38, 1967, pp. 916-918. | MR 210166 | Zbl 0201.51104

[21] J.B. Robertson, Independence and Fair Coin-Tossing, Math. Scientist, Vol. 10, 1985, pp. 109-117. | MR 832126 | Zbl 0583.60031

[22] J.B. Robertson et J.M. Womack, A pairwise independent stationary stochastic process, Statistics and Probability Letters, Vol. 3, 1985, pp. 195-199. | MR 801689 | Zbl 0569.60041

[23] M. Rosenblatt et D. Slepian, Nth order Markov chain with every N variables independent, J. SIAM, Vol. 10, 1962, pp. 537-549. | MR 150824 | Zbl 0154.43103

[24] J.M. Stoyanov, Counterexamples in probability, John Wiley & Sons, 1987. | Zbl 0629.60001