Geodesic
Estimates of speed of convergence in limit theorems for first passage times
Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 487-495.

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In this article there are proven nonuniform estimates of speed of convergence in limit theorems for maximum sums of independent terms. The results thus obtained are applied to estimating speed of convergence in limit theorems for first passage times in random walks generated by these sums. 
@article{MZM_1978_23_3_a15,
     author = {Sh. A. Mirakhmedov},
     title = {Estimates of speed of convergence in limit theorems for first passage times},
     journal = {Matemati\v{c}eskie zametki},
     pages = {487--495},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a15/}
}
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Sh. A. Mirakhmedov. Estimates of speed of convergence in limit theorems for first passage times. Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 487-495. http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a15/