Geodesic
On the Maximum Partial Sums of Sequences of Independent Random Variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 4, pp. 398-404

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In the present work the results of K. L. Chung [2] concerning the maximum partial sums of sequences of independent random variables are obtained for a weaker condition. The method employed in the proof is analogous to the one used by Chung with the difference that, instead of Esseen’s approximations involving third moments, we use Berry’s approximations involving only second moments. 
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     author = {R. P. Pakshirajan},
     title = {On the {Maximum} {Partial} {Sums} of {Sequences} of {Independent} {Random} {Variables}},
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R. P. Pakshirajan. On the Maximum Partial Sums of Sequences of Independent Random Variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 4, pp. 398-404. http://geodesic.mathdoc.fr/item/TVP_1959_4_4_a1/