Abstract:
We investigate the asymptotic behavior almost surely of the large increments (that is, exceeding in order the logarithm) of sums of nonidentically distributed random variables with zero means, finite variances, and the moment generating functions being finite within an interval with the left end at zero. The theorems obtained generalize the known results of Csorgo and Revesz.
Keywords:increments of sums of independent random variables, large increments, strong approximation laws, Erdos–Renyi law, Shepp law.
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