zbMATH — the first resource for mathematics

Central limit theorems and weak laws of large numbers in certain Banach spaces. (English) Zbl 0488.60009

60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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., Araujo, A., Gin?, E.: On Poisson measures, Gaussian measures and the central limit theorem in Banach spaces. Adv. in Probability, Vol. IV (Probability in Banach spaces, J. Kuelbs, ed.) 1-68. New York: Dekker 1978
[3] de Acosta, A., Gin?, E.: Convergence of moments and related functionals in the central limit theorem in Banach spaces. Z. Wahrscheinlichkeitstheorie verw. Geb. 48, 213-231 (1979) · Zbl 0388.60008
[4] Araujo, A., Gin?, E.: On tails and domains of attraction of stable measures on Banach spaces. Trans. Amer. Math. Soc. 248, 105-119 (1979) · Zbl 0408.60007
[5] Araujo, A., Gin?, E.: The central limit theorem for real and Banach valued random variables. New York: Wiley 1980 · Zbl 0457.60001
[6] Chobanian, S.A., Tarieladze, V.I.: A counterexample concerning CLT in Banach spaces. Lecture Notes in Math. 656, 25-30. Berlin-Heidelberg-New York: Springer 1978
[7] Denker, M., Kombrink, R.: On B-convex Orlicz spaces. Lecture Notes in Math. 709, 87-96. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0426.46017
[8] Figiel, T.: On the moduli of convexity and smoothness. Studia Math. 56, 121-155 (1976) · Zbl 0344.46052
[9] Gin?, E.: Domains of attraction in Banach spaces. Lecture Notes in Math. 721, 22-40. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0406.60006
[10] Gin?, E.: Sums of independent random variables and sums of their squares. Publ. Mat. Univ. Aut?noma de Barcelona 22, 127-132 (1980)
[11] Gin?, E., Mandrekar, V., Zinn, J.: On sums of independent random variables with values in L p, p?2. Lecture Notes in Math. 709, 111-124. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0424.60004
[12] Gin?, E., Marcus, M.B.: Some results on the domain of attraction of stable measures in C(K). [Probability and Math. Statist. To appear ] · Zbl 0535.60010
[13] Hoffmann-J?rgensen, J.: Sums of independent Banach space valued random variables. Studia Math. 52, 159-186 (1974) · Zbl 0265.60005
[14] Hoffmann-J?rgensen, J., Pisier, G.: The law of large numbers and the central limit theorem in Banach spaces. Ann. Probab. 4, 587-599 (1976) · Zbl 0368.60022
[15] Johnson, W.B.: Banach spaces all of whose subspaces have the approximation property. Special topics of Applied Mathematics (Frehse et al., ed.), 14-26. Amsterdam: North Holland 1980 · Zbl 0441.46014
[16] Jain, N.: Central limit theorem and related questions in Banach spaces. Proc. Symp. in Pure Math. XXXI, 55-65. Amer. Math. Soc., Providence, R.I, 1977
[17] Klass, M.: Precision bounds for the relative error in the approximation of E?S n? and extensions. Ann. Probab. 8, 350-367 (1980) · Zbl 0428.60058
[18] Krasnoselskii, M.A., Rutikii, Y.B.: Convex functions and Orlicz spaces. Groningen 1961 [Transl. from Russian]
[19] Krivine, J.L.: Th?or?mes de factorisation dans les espaces reticul?s. S?minaire Maurey-Schwartz 1973-74. Exp. XXII et XXIII. Ecole Polytechnique, Paris
[20] Kuelbs, J., Zinn, J.: Some results on LIL behavior. To appear in Ann. Probab. · Zbl 0518.60009
[21] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces I. Berlin-Heidelberg-New York: Springer 1977 · Zbl 0362.46013
[22] Lindenstrauss, J., Tsafriri, L.: Classical Banach spaces II. Berlin-Heidelberg-New York: Springer 1979
[23] Mandrekar, V., Zinn, J.: Central limit theorem for symmetric case: convergence to nonGaussian laws. Studia Math. 67, 279-296 (1980) · Zbl 0461.60022
[24] Marcus, M., Woyczynski, W.: Stable measures and central limit theorems in spaces of stable type. Trans. Amer. Math. Soc. 251, 71-101 (1979) · Zbl 0449.60003
[25] Maurey, B.: Type et cotype dans les espaces minis de structures locales inconditionelles. S?minaire Maurey-Schwartz 1973-74. Exp. XXIV et XXV. Ecole Polytechnique, Paris
[26] Maurey, B., Pisier, G.: S?ries de variables al?atoires independentes et propriet?s g?om?triques des espaces de Banach. Studia Math. 58, 45-90 (1976) · Zbl 0344.47014
[27] Mourier, E.: Elements al?atoires ? valeurs dans un espace de Banach. Ann. Inst. H. Poincar? 13, 159-244 (1953) · Zbl 0053.09503
[28] Pisier, G.: Le th?or?me limite central et la loi du logaritme iter? dans les espaces de Banach. S?minaire Maurey-Schwartz 1975-76. Exp. III et IV. Ecole Polytechnique, Paris
[29] Pisier, G., Zinn, J.: On the limit theorems for random variables with values in L p, p?2. Z. Wahrscheinlichkeitstheorie verw. Gebiete 41, 289-304 (1978) · Zbl 0364.60031
[30] Ra?kauskas, A.: A remark on stable measures on Banach spaces. Lithuanian Math. J. 19, 267-270 (1979) · Zbl 0447.28011
[31] Reisner, S.: A factorization theorem in Banach lattices and its application to Lorentz spaces. Ann. Inst. Fourier (Grenoble) 31, 239-255 (1981) · Zbl 0437.46025
[32] Rosenthal, H.: On the span in L pof sequences of independent random variables. Proc. Sixth Berkeley Sympos. on Math. Statist. and Probab. Vol. II, 149-167. Univ. of California Press, Berkeley (1972)
[33] Woyczynski, W.: Geometry and martingales in Banach spaces. Part II: independent increments. Adv. in Probability, Vol. 4 (Probability in Banach spaces, J. Kuelbs ed.) 267-518. New York: Dekker 1978
[34] Zinn, J.: Inequalities in Banach spaces with applications to probabilistic limit theorems: a survey. Lecture Notes in Math. 860, 324-329. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0482.60009
[35] Marcus, M.B., Pisier, G.: Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes (1982). Preprint. · Zbl 0547.60047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.