Some results on two-sided LIL behavior

Details Some results on two-sided LIL behavior Some results on two-sided LIL behavior

2005-07-22

arxiv.org/abs/math/0507462v1

Annals of Probability 2005, Vol. 33, No. 4, 1601-1624

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117905000000198 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117905000000198

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, 01 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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