Théorème limite central dans les espaces l p (B)(1p<)
Ledoux, M.
Annales de l'I.H.P. Probabilités et statistiques, Tome 19 (1983), p. 393-411 / Harvested from Numdam
Publié le : 1983-01-01
@article{AIHPB_1983__19_4_393_0,
     author = {Ledoux, Michel},
     title = {Th\'eor\`eme limite central dans les espaces $l\_p(B) (1 \le p < \infty )$},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {19},
     year = {1983},
     pages = {393-411},
     zbl = {0527.60007},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1983__19_4_393_0}
}
Ledoux, M. Théorème limite central dans les espaces $l_p(B) (1 \le p < \infty )$. Annales de l'I.H.P. Probabilités et statistiques, Tome 19 (1983) pp. 393-411. http://gdmltest.u-ga.fr/item/AIHPB_1983__19_4_393_0/

[1] A. De Acosta, A. Araujo, E. Giné, On Poisson measures, Gaussian measures and the central limit theorem in Banach spaces. Dekker, New York, Adv. in Probability, t. 4, 1978, p. 1-68. | MR 515429

[2] A. De Acosta, J. Kuelbs, Some results on the cluster set C({Sn/an}) and the LLI. Ann. Probability, t. 11, 1983, p. 102-122. | MR 682803 | Zbl 0507.60002

[3] A. Araujo, E. Giné, The central limit theorem for real and Banach valued random variables. Wiley, New York, 1980. | MR 576407 | Zbl 0457.60001

[4] S.A. Chobanyan, V.I. Tarieladze, Gaussian characterization of certain Banach spaces. J. Multivariate Anal., t. 7, 1977, p. 183-203. | MR 433572 | Zbl 0362.60054

[5] S.A. Chobanyan, V.I. Tarieladze, A counterexample concerning cli in Banach spaces. Probability theory on vector spaces, Poland, 1977. Springer, Berlin-Heidelberg-New York, Lecture Notes in Math., t. 656, 1978, p. 25-30. | Zbl 0386.60007

[6] X. Fernique, Régularité des trajectoires des fonctions aléatoires gaussiennes. École d'été de Probabilités de St-Flour, 1974. Springer, Berlin-Heidelberg-New York. Lecture Notes in Math., t. 480, 1975, p. 1-96. | MR 413238 | Zbl 0331.60025

[7] E. Giné, J. Zinn, Central limit theorems and weak laws of large numbers in certain Banach spaces. Zeitschrift für Wahr, t. 62, 1983, p. 323-354. | MR 688642 | Zbl 0488.60009

[8] V. Goodman, J. Kuelbs, J. Zinn, Some results on the law of the iterated logarithm with applications to weighted empirical processes. Ann. Probability, t. 9, 1981, p. 713-752. | MR 628870 | Zbl 0472.60004

[9] B. Heinkel, Relation entre théorème central-limite et loi du logarithme itéré dans les espaces de Banach. Zeitschrift für Wahr., t. 49, 1979, p. 211-220. | MR 543994 | Zbl 0397.60018

[10] J. Hoffmann-Jørgensen, Sums of independent Banach space valued random variables. Studia Math., t. 52, 1974, p. 159-186. | MR 356155 | Zbl 0265.60005

[11] J. Hoffmann-Jørgensen, G. Pisier, The law of large numbers and the central limit theorem in Banach spaces. Ann. Probability, t. 4, 1976, p. 587-599. | MR 423451 | Zbl 0368.60022

[12] N.C. Jain, Central limit theorem and related questions in Banach spaces. Proc. Symp. in Pure Math., t. XXXI, 1977, p. 55-65, Amer. Math. Soc., Providence R. I. | MR 451328 | Zbl 0389.60002

[13] R.C. James, Some self dual properties of normed linear spaces. Ann. Math. Studies, t. 69, 1972, p. 159-176. | MR 454600 | Zbl 0233.46025

[14] J. Kuelbs, Kolmogorov's law of the iterated logarithm for Banach space valued random variables. Illinois J. Math., t. 21, 1977, p. 784-800. | MR 455061 | Zbl 0392.60010

[15] V.V. Kvaratskheliya, Nguyen Xuy Tien, The central limit theorem and the strong law of large numbers in the spaces lp(X), 1 ≤ p < ∞. Theor. Probability Appl., t. 21, 1976, p. 780-790. | Zbl 0382.60024

[16] S. Kwapien, Isomorphic characterization of inner product spaces by orthogonal series with vector valued coefficients. Studia Math., t. 44, 1972, p. 583-595. | MR 341039 | Zbl 0256.46024

[17] M. Ledoux, Sur les théorèmes limites dans certains espaces de Banach lisses. Probability in Banach spaces IV, Oberwolfach, 1982. Springer, Berlin-Heidelberg-New York, Lecture Notes in Math., t. 990, 1983, p. 150-169. | MR 707515 | Zbl 0516.60004

[18] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces II. Springer, Berlin-Heidelberg-New York, 1979. | MR 540367 | Zbl 0403.46022

[19] B. Maurey, G. Pisier, Séries de variables aléatoires vectorielles indépendantes èt propriétés géométriques des espaces de Banach. Studia Math., t. 58, 1976, p. 45-90. | MR 443015 | Zbl 0344.47014

[20] G. Pisier, Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach. Séminaire Maurey-Schwartz, 1975-1976, exposés 3, 4 et appendice, École Polytechnique, Paris, 1976. | Numdam | Zbl 0403.60011

[21] G. Pisier, J. Zinn, On the limit theorems for random variables with values in the spaces Lp (2 ≤ p < ∞). Zeitschrift für Wahr., t. 41, 1977, p. 289-304. | Zbl 0364.60031

[22] N.V. Vakhania, Sur une propriété des répartitions normales de probabilités dans les espaces lp (1 ≤ p < ∞) et H. C. R. Acad. Sci. Paris, Série A, t. 260, 1965, p. 1334- 1336. | Zbl 0132.13003

[23] J. Zinn, Inequalities in Banach spaces with applications to probabilistic limit theorems: a survey. Probability in Banach spaces III, Medford, 1980. Springer, Berlin-Heidelberg-New York, Lecture Notes in Math., t. 860, 1981, p. 324-329. | MR 647974 | Zbl 0482.60009