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Some results on two-sided LIL behavior

Uwe Einmahl·Deli Li
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Abstract

Let {X,X_n;n\geq 1} be a sequence of i.i.d. mean-zero random variables, and let S_n=\sum_{i=1}^nX_i,n\geq 1. We establish necessary and sufficient conditions for having with probability 1, 0 1 and to h(n)=(\log n)^r, r>0, we obtain analogues of the Hartman-Wintner LIL in the infinite variance case. Our proof is based on a general result dealing with LIL behavior of the normalized sums {S_n/c_n;n\ge 1}, where c_n is a sufficiently regular normalizing sequence.

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Uwe Einmahl, Deli Li. 2005-07-22. Some results on two-sided LIL behavior. https://doi.org/10.1214/009117905000000198

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