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On complete convergence for arrays of rowwise independent random elements in Banach spaces. (English) Zbl 0940.60032
The authors provide results on complete convergence for arrays of rowwise independent Banach space valued random variables. Conditions are rather in terms of truncated moments than of the moments themselves.
Reviewer: A.Gut (Uppsala)

MSC:
60F15 Strong limit theorems
60G50 Sums of independent random variables; random walks
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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References:
[1] De Acosta A., Ann.Probab 9 pp 157– (1981) · Zbl 0449.60002
[2] Araujo A., The central Limit Theorem for Real and Banach Valued Random Variables (1980) · Zbl 0457.60001
[3] Adler A., Bull. Inst. Math. Acad. Sinica 27 (1999)
[4] Adler A., Internat. J. Math. & Math. Sci 18 pp 33– (1995) · Zbl 0822.60024
[5] Berger E., Ann. Probab 19 pp 1206– (1991) · Zbl 0757.60002
[6] Bozorgnia A., Internat. J. Math. & Math. Sci 16 pp 587– (1993) · Zbl 0844.60005
[7] Chow Y.S., Probability Theory: Independence, Inter-changeability, Martingales (1997)
[8] Erdös P., Ann. Math. Statis 20 pp 286– (1949) · Zbl 0033.29001
[9] Etemadi N., Sankhyā Ser. A 47 pp 215– (1985)
[10] Gut A., Ann. Probab 13 pp 1286– (1985) · Zbl 0582.60057
[11] Gut A., Periodica Math. Hungarica 2 pp 51– (1992) · Zbl 0760.60029
[12] Hoffmann-Jgensen J., Studia Math 52 pp 159– (1974)
[13] Hsu P.L., Proc. Nat. Acad. Sci. U.S.A 33 pp 25– (1947) · Zbl 0030.20101
[14] Hu T.C., Acta Math. Acad. Sci. Hungar 54 pp 153– (1989) · Zbl 0685.60032
[15] Hu T.C., Statist. Probab. Lett 38 pp 27– (1998) · Zbl 0910.60017
[16] Jain N., Z. Wahrsch. Verw. Gebiete 33 pp 155– (1975) · Zbl 0304.60033
[17] Kuczmaszewska A., Internat. J. Math. & Math. Sci 17 pp 1– (1994) · Zbl 0798.60006
[18] Kuelbs J., Ann. Probab 7 pp 75– (1979) · Zbl 0399.60007
[19] Loéve M., Probability Theory I (1977)
[20] Pruitt W.E., J. Math. Mech 15 pp 769– (1966)
[21] Rohatgi V.K., Proc. Cambridge Philos. Soc 69 pp 305– (1971)
[22] Stout W.F., Almost Sure Convergence (1974) · Zbl 0321.60022
[23] Sung S.H., Stochastic Anal. Appl 15 pp 255– (1997) · Zbl 0902.60011
[24] Taylor R.L., Lecture Notes in Mathematics 672 (1978)
[25] Taylor R.L., Internat. J. Math. & Math. Sci 10 pp 805– (1987) · Zbl 0628.60011
[26] Wang X., Stochastic Anal. Appl 11 pp 115– (1993) · Zbl 0764.60037
[27] Wei D., Bull. Inst. Math. Acad. Sinica 6 pp 49– (1978)
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