Large deviations in the central limit theorem for endomorphisms of Euclidean space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 1, pp. 195-210
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Let $W$ be such a nonsingular integer matrix that $|\operatorname{det}W|>1$; $f$ is a real-valued periodic for every argument Lipschitz-continuous function defined on the unit hypercube from $R^d$. For a sequence $(f(tW^n))$, we prove the central limit theorem with large deviations within the interval $[1;\mathrm o(n^{1/8}/\ln n)]$.
Keywords:
limit theorem, endomorphisms, large deviations.
@article{UZKU_2011_153_1_a15,
author = {V. T. Dubrovin},
title = {Large deviations in the central limit theorem for endomorphisms of {Euclidean} space},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {195--210},
publisher = {mathdoc},
volume = {153},
number = {1},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a15/}
}
TY - JOUR AU - V. T. Dubrovin TI - Large deviations in the central limit theorem for endomorphisms of Euclidean space JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2011 SP - 195 EP - 210 VL - 153 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a15/ LA - ru ID - UZKU_2011_153_1_a15 ER -
%0 Journal Article %A V. T. Dubrovin %T Large deviations in the central limit theorem for endomorphisms of Euclidean space %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2011 %P 195-210 %V 153 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a15/ %G ru %F UZKU_2011_153_1_a15
V. T. Dubrovin. Large deviations in the central limit theorem for endomorphisms of Euclidean space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 1, pp. 195-210. http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a15/