Geodesic
A converse to the law of the iterated logarithm for random walk
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 2, pp. 364-366

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Let $\{S_n\}$ be a random walk with independent increments. Then $\mathbf{E}S_1=0$, $\mathbf{E}S_1^2=1$ iff $$ \limsup_{n\to\infty}\frac{S_n}{\sqrt{2n\log\log n}}=1\qquad\text{almost surely.} $$ 
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     author = {A. I. Martikaǐnen},
     title = {A converse to the law of the iterated logarithm for random walk},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {364--366},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a11/}
}
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A. I. Martikaǐnen. A converse to the law of the iterated logarithm for random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 2, pp. 364-366. http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a11/