Abstract. For a sequence of real-valued i.i.d. mean $0$ random variables $\{X, X_{n}; n \geq1 \} $ with partial sums $S_{n} = \sum_{i=1}^n X_{i}$, $n \geq1$, conditions are provided for $\{X, X_{n}; n \geq1 \} $ to enjoy one-sided iterated logarithm type behavior of the form $0 < \limsup_{n \rightarrow\infty } S_{n}/\sqrt{nh(n)} < \infty $ almost surely where $h(\cdot )$ is a positive, nondecreasing function which is slowly varying at infinity. New results are obtained as special cases and some open problems are posed.
AMS Subject Classification
(1991): 60F15, 60G50
Keyword(s):
Sums of i.i.d. random variables,
law of the iterated logarithm,
one-sided iterated logarithm type behavior,
almost surely,
slowly varying function
Received January 4, 2007, and in revised form May 10, 2007. (Registered under 5971/2009.)
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