Geodesic
Limit theorems for the first passage times of a~certain level
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 417-420

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Let $\{X_n\}_{n=1,2,\dots,}$ be a sequence of i.i.d.r.v.'s and $T(r)=\min\{k\ge 1:X_1+\dots+X_k\ge r\}$ be the first passage time of a level $r>0$. Two estimates are obtained for the rate of convergence of $T(r)$ to limit laws as $r\to\infty$. 
@article{TVP_1976_21_2_a20,
     author = {N. I. Migaǐ and V. B. Nevzorov},
     title = {Limit theorems for the first passage times of a~certain level},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {417--420},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a20/}
}
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N. I. Migaǐ; V. B. Nevzorov. Limit theorems for the first passage times of a~certain level. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 417-420. http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a20/