Geodesic
Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 366-372

Voir la notice de l'article provenant de la source Math-Net.Ru

The asymptotic behavior as $n\to\infty$ of the normed sums $\sigma_n=n^{-1}\sum_{k=0}^{n-1}X_k$ for a stationary process $X=(X_n, n\in\mathbb Z)$ is studied. For a fixed $\varepsilon>0$, upper estimates for $\mathsf P\bigl(\sup_{k\ge n} |\sigma_k|\ge\varepsilon\bigr)$ as $n\to\infty$ are obtained. 
@article{MZM_1998_64_3_a3,
     author = {V. F. Gaposhkin},
     title = {Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {366--372},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a3/}
}
TY  - JOUR
AU  - V. F. Gaposhkin
TI  - Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes
JO  - Matematičeskie zametki
PY  - 1998
SP  - 366
EP  - 372
VL  - 64
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a3/
LA  - ru
ID  - MZM_1998_64_3_a3
ER  - 
%0 Journal Article
%A V. F. Gaposhkin
%T Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes
%J Matematičeskie zametki
%D 1998
%P 366-372
%V 64
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a3/
%G ru
%F MZM_1998_64_3_a3
V. F. Gaposhkin. Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 366-372. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a3/