Geodesic
Functional law of the iterated logarithm for truncated sums
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 126-142

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We obtain the functional law of the iterated logarithm (the FLIL) for truncated sums $S_n=\sum\limits_{j=1}^n\,X_j\,I\{X^2_j\le b_n\}$ of independent symmetric random variables $X_j$, $1\le j\le n$, $b_n\le\infty$. Considering the random normalization by $$ T^{1/2}_n=\Bigl(\sum_{j=1}^n\,X^2_j\,I\{X^2_j\le b_n\}\Bigr)^{1/2} $$ we get the upper estimate in the FLIL using only the condition that $T_n\to\infty$ a.s. These results are useful for studing trimmed sums. 
@article{ZNSL_1997_244_a7,
     author = {V. A. Egorov and V. I. Pozdnyakov},
     title = {Functional law of the iterated logarithm for truncated sums},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {126--142},
     publisher = {mathdoc},
     volume = {244},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a7/}
}
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V. A. Egorov; V. I. Pozdnyakov. Functional law of the iterated logarithm for truncated sums. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 126-142. http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a7/