Abstract
Let { S n , n ⩾ } denote the partial sums of a sequence of independent random variables, and let ( B n , n ⩾ 1) be a non-decreasing sequence with B n → ∞. Upper and lower bounds for lim sup n → ∞ S n /(2 B 2 n log log B 2 n ) 1 2 are presented.
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