Geodesic
Notes on inequalities for sums of independent variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 588-590

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In this paper we note that the inequalities of [1], [2] will also remain valid for the maximum of sequential sums: $\zeta_n=\max\limits_{k\le n}S_k$. 
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     author = {A. A. Borovkov},
     title = {Notes on inequalities for sums of independent variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {588--590},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_3_a19/}
}
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A. A. Borovkov. Notes on inequalities for sums of independent variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 588-590. http://geodesic.mathdoc.fr/item/TVP_1972_17_3_a19/