Geodesic
A note on the rate of convergence in stability theorems
Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 119-120

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The note contains an example showing that the estimates (2)–(4) of the rate of convergence in stability theorems for supremum of partial sums of i. i. d. random variables are unimprovable. 
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     author = {K. A. Borovkov},
     title = {A note on the rate of convergence in stability theorems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {119--120},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a10/}
}
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K. A. Borovkov. A note on the rate of convergence in stability theorems. Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 119-120. http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a10/