Summary
New upper and lower exponential bounds are obtained under a more general condition than that of Kolmogorov and these, in turn, elicit iterated logarithm laws
for a wider class of bounded, mean zero, independent random variables {X n , n≧1}. The constant C need not be the universal number 2 1/2 and may depend upon the underlying distributions. Upper and lower bounds are provided for C in terms of a parameter. The upper bound is also exploited in proving a new strong law of large numbers for independent random variables.
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Research supported by National Science Foundation under Grant Number MCS 78-00805
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Teicher, H. Generalized exponential bounds, iterated logarithm and strong laws. Z. Wahrscheinlichkeitstheorie verw Gebiete 48, 293–307 (1979). https://doi.org/10.1007/BF00537526
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DOI: https://doi.org/10.1007/BF00537526