Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
de Acosta, A. (1970). Existence and convergence of probability measures in Banach spaces. Trans. Amer. Math. Soc. 152, 273–298.
de Acosta, A. (1979). Exponential moments of vector valued random series and triangular arrays. Ann. Probability.
de Acosta, A. (1979). On the general converse CLT in Banach spaces. Probabilityin Banach spaces II, Lect. Notes in Math. 709, 1–8.
de Acosta, A. (1979). Strong exponential integrability of sums of independent B-valued random vectors. Probability and Math. Stat., to appear.
de Acosta, A.; Araujo, A.; Giné, E. (1978). Poisson measures, Gaussian measures and the central limit theorem in Banach spaces. Advances in Probability, Vol IV, 1–68. (Kuelbs ed.) Dekker, New York.
de Acosta, A. and Giné, E. (1979). Convergence of moments and related functionals in the central limit theorem in Banach spaces. Z. Wahrscheinlichkeitstheorie verw. Gebiete 48, 213–231.
de Acosta, A. and Samur, J. (1979). Infinitely divisible probability measures and the converse Kolmogorov inequality in Banach spaces. Studia Math. 56, 143–160.
Araujo, A. (1979). On the central limit theorem in Banach spaces. J. Multivariate Analysis 8, 598–613.
Araujo, A. and Giné, E. (1979). On tails and domains of attraction of stable measures in Banach spaces. Trans. Amer. Math. Soc. 248, 105–119.
Araujo, A. and Giné, E. (1980). The central limit theorem for real and Banach valued random variables. Wiley, New York.
Araujo, A.; Giné, E.; Mandrekar, V.; Zinn, J. (1978). On the validity of the accompanying laws theorem in Banach spaces. Ann. Probability, to appear.
Dettweiler, E. (1976). Grenswertsätze fur Wahrscheinlichkeitsmasse auf Badrikianschen Raumen. Z. Wahrscheinlichkeitstheorie verw. Gebiete 34, 285–311.
Fernique, X. (1978). Continuité et théorème limite central pour les transformées de Fourier des mesures aléatoires du second ordre. Z. Wahrscheinlichkeitstheorie verw. Gebiete 42, 57–66.
Giné, E. (1979). Domains of attraction in Banach spaces. Strasbourg Probability Seminar, 1978. Lect. Notes in Math. 721, 22–40.
Giné, E. (1980). Domains of partial attraction in several dimensions. Ann. Inst. H. Poincaré XVI, 87–100.
Giné, E.; Mandrekar, V.; Zinn, J. (1979). On sums of independent random variables with values in Lp, 2≤p<∞. Probability in Banach spaces II. Lect. Notes in Math. 709, 111–124.
Giné, E. and Marcus, M. (1979). Some results on the domain of attraction of stable measures on C(K). Probability and Math. Stat., to appear.
Giné, E. and Marcus, M. (1980). On the general central limit theorem in C(K). Proc. CNRS Int. Probability Coll., St. Flour 1980. Lect. Notes in Math., to appear.
Giné, E. and Zinn, J. (1980). Manuscript.
Hoffmann-Jorgensen, J. (1974). Sums of independent Banach space valued random variables. Studia Math. 52, 159–186.
Hoffmann-Jorgensen, J. and Pisier, G. (1976). The law of large numbers and the central limit theorem in Banach spaces. Ann. Probability 4, 587–599.
Jain, N. (1977). Central limit theorems and related questions in Banach spaces. Proc. Symp. in Pure Math. XXXI, 55–65. Amer. Math. Soc., Providence, R.I.
LeCam, L. (1970). Remarques sur le théorème limite central dans les espaces localement convexes. Proc. Int. Coll. sur Les Probabilités sur les structures algebriques. CNRS, Paris. 233–249.
Mandrekar, V. and Zinn, J. (1979). Central limit problem in symmetric case: convergence to non-Guassian laws. Studia Math., to appear.
Marcus, M.B. (1978). Continuity and central limit theorem for random trigonometric series. Z. Wahrscheinlichkeitstheorie verw. Gebiete 42, 35–56.
Parthasarathy, K. R. (1967). Probability measures on metric spaces. Academic Press, New York.
Pisier, G. (1975). Le théorème limite central et la loi du logarithme itere dans les espaces de Banach. Sem. Maurey-Schwartz 1975–76, exp. III et IV.
Pisier, G. (1980). Semigroupes holomorphes et geometrie des espaces de Banach. Comp. Rend. Acad. Sci. Paris, to appear.
Pisier, G. and Zinn, J. (1978). On the limit theorems for random variables with values in Lp, 2≤p<∞. Z. Wahrscheinlichkeitstheorie verw. Gebiete 41, 289–304.
Woyczynsky, W. A. (1978). Geometry and martingales in Banach spaces, part II: independent increments. Advances in Probability, Vol. IV, 267–517. (J. Kuelbs ed.). Dekker, New York.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Gine, E. (1981). Central limit theorems in Banach spaces: A survey. In: Beck, A. (eds) Probability in Banach Spaces III. Lecture Notes in Mathematics, vol 860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090613
Download citation
DOI: https://doi.org/10.1007/BFb0090613
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10822-1
Online ISBN: 978-3-540-38710-7
eBook Packages: Springer Book Archive