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Convergence of moments and related functionals in the central limit theorem in Banach spaces. (English) Zbl 0388.60008

60B10 Convergence of probability measures
60F05 Central limit and other weak theorems
Full Text: DOI
[1] de Acosta, A.: Existence and convergence of probability measures in Banach spaces. Trans. Amer. Math. Soc.152, 273–298 (1970) · Zbl 0226.60007
[2] de Acosta, A.: Exponential moments of vector-valued random series and triangular arrays (To appear in Ann. Probability 1979) · Zbl 0435.60004
[3] de Acosta, A., Araujo, A., Giné, E.: On Poisson measures, Gaussian measures and the central limit theorem in Banach spaces. Advances in Probability,4, 1–68. New York: M. Dekker 1978
[4] Agnew, G.: Global versions of the central limit theorem. Proc. Nat. Acad. Sci. USA.40, 800–804 (1954) · Zbl 0055.36703
[5] Araujo, A., Giné, E.: On tails and domains of attraction of stable measures in Banach spaces. To appear in Trans. Amer. Math. Soc. 1979 · Zbl 0408.60007
[6] Feller, W.: An introduction to Probability Theory and its applications, Vol. II, Second Edition. New York: Wiley 1971 · Zbl 0219.60003
[7] Giné, E., León, J.R.: On the central limit theorem in Hilbert space. Proc. First Conference on Math. at the Service of Man, Barcelona 1977 (To appear in 1979)
[8] Hoffmann-Jorgensen, J.: Sums of independent Banach space valued random variables. Studia Math.52, 159–186 (1974) · Zbl 0265.60005
[9] Jain, N.: Central limit theorem and related questions in Banach space. Proceedings of Symposia in Pure Mathematics, Vol. XXI, 55–65. Amer. Math. Soc., Providence, R. I. (1977) · Zbl 0389.60002
[10] Kruglov, V.N.: Convergence of numerical characteristics of sums of independent random variables with values in a Hilbert space. Theor. Probability Appl.18, 694–712 (1973) · Zbl 0321.60045
[11] Kruglov, V.M.: Convergence of numeric characteristics of sums of independent random variables and global limit theorems. Proc. 2nd. Japan-USSR Probability Sympos. Lecture Notes in Math.33, 255–296. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0264.60015
[12] Kruglov, V.M.: Global limit theorems. Theor. Probability Appl. XXI, 125–129 (1976) · Zbl 0366.60075
[13] Loève, M.: Probability Theory (2nd. Edition). Princeton: Van Nostrand 1960 · Zbl 0095.12201
[14] Maejima, M.: SomeL p versions for the central limit theorem. Ann. Probability6, 341–344 (1978) · Zbl 0389.60014
[15] Marti, J.T.: Introduction to the theory of bases. Berlin-Heidelberg-New York: Springer 1969 · Zbl 0191.41301
[16] Maurey, B., Pisier, G.: Séries de variables aléatoires vectorielles independentes et proprietés géométriques des espaces de Banach. Studia Math.58, 45–90 (1976) · Zbl 0344.47014
[17] Parthasarathy, K.R.: Probability measures on metric spaces. New York: Academic Press 1967 · Zbl 0153.19101
[18] Petrov, V.V.: Sums of independent random variables. Berlin-Heidelberg-New York: Springer 1975 · Zbl 0322.60043
[19] Pisier, G.: Le théoreme de la limite centrale et la loi du logarithme iteré dans les espaces de Banach. Séminaire Maurey-Schwartz 1975, Exp. III (1975)
[20] Prohorov, Y.V.: An extremal problem in Probability Theory. Theor. Probability Appl.4, 201–203 (1959) · Zbl 0093.15102
[21] Stout, W.: Almost sure convergence. New York: Academic Press 1974 · Zbl 0321.60022
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