Geodesic
On asymptotics of large deviation probabilities of sums~$\Sigma f(x2^n)$
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 243-253

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In the paper, large deviations in limit theorems for sums $\sum_nf(x2^n)$ where $f(t)$ satisfies a Lipschitz condition, are investigated. A result is obtained for the narrow zone $[0,o((N/\ln^2N)^{1/4})]$. For the particular case $f(t)=\{t\}$ by a special method, a result for $[0,o(\sqrt N)]$ is obtained. 
@article{TVP_1970_15_2_a5,
     author = {D. A. Moskvin},
     title = {On asymptotics of large deviation probabilities of sums~$\Sigma f(x2^n)$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {243--253},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a5/}
}
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D. A. Moskvin. On asymptotics of large deviation probabilities of sums~$\Sigma f(x2^n)$. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 243-253. http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a5/