Abstract
Let ${X_n, 1 \leq n < \infty}$ be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index $0 < \alpha < 2$. The limit of $x_n^{-1}\log P{S_n/ \max |X_i| \geq x_n}$ is found when $x_n \to \infty$ and $\x_n/n \to 0$. The large deviation result is used to prove the law of the iterated logarithm for the self-normalized partial sums.
Citation
Lajos Horváth. Qi-Man Shao. "Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation." Ann. Probab. 24 (3) 1368 - 1387, July 1996. https://doi.org/10.1214/aop/1065725185
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