Geodesic
Limit Theorems on the Distribution of Maximum of Sums of Bounded, Lattice Random Variables. II
Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 4, pp. 377-392
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The second part of this paper contains the proofs of integral theorems concerning $$\bar s_n=\max\left({\xi_1+\xi_2 +\cdots+\xi_\nu}\right),\quad1\leq\nu\leq n$$ where $\xi_i$ are bounded, lattice, independent and identically distributed random variables. 
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     author = {A. A. Borovkov},
     title = {Limit {Theorems} on the {Distribution} of {Maximum} of {Sums} of {Bounded,} {Lattice} {Random} {Variables.~II}},
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A. A. Borovkov. Limit Theorems on the Distribution of Maximum of Sums of Bounded, Lattice Random Variables. II. Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 4, pp. 377-392. http://geodesic.mathdoc.fr/item/TVP_1960_5_4_a0/