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Approximation of partial sums of i.i.d. r.v.s when the summands have only two moments. (English) Zbl 0338.60032

MSC:
60G50 Sums of independent random variables; random walks
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[1] Heyde, C.C.: Some properties of metrics in a study on convergence to normality. Z. Wahrscheinlichkeitstheorie verw. Gebiete 11, 181-192 (1969) · Zbl 0169.20902 · doi:10.1007/BF00536379
[2] Komlós, J., Major, P., Tusnády, G.: An approximation of Partial Sums of Independent RV’s and the Sample D.F. (II). Z. Wahrscheinlichkeitstheorie verw. Gebiete 34, 33-58 (1976) · Zbl 0307.60045 · doi:10.1007/BF00532688
[3] Major, P.: The approximation of partial sums of independent RV’s. Z. Wahrscheinlichkeitstheorie verw. Gebiete 35, 213-220 (1976) · Zbl 0338.60031 · doi:10.1007/BF00532673
[4] Loève, M.: Probability Theory. Toronto-New York-London: Van Nostrand 1963 · Zbl 0095.12201
[5] Strassen, V.: An invariance principle for the law of iterated logarithm. Z. Wahrscheinlichkeitstheorie verw. Gebiete 3, 211-226 (1964) · Zbl 0132.12903 · doi:10.1007/BF00534910
[6] Wichura, M.J.: Inequalities with application to weak convergence of random processes with multi-dimensional time parameters. Ann. Math. Statist. 40, 681-687 (1969) · Zbl 0214.17701 · doi:10.1214/aoms/1177697741
[7] Wichura, M.J.: Some Strassen type laws of the iterated logarithm for multiparameter stochastic processes. Ann. Probab. 1, 272-296 (1973) · Zbl 0288.60030 · doi:10.1214/aop/1176996980
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