Geodesic
Large Deviations and the Rate of Convergence in the Birkhoff Ergodic Theorem
Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 569-577

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

For bounded averaged functions, we prove the equivalence of the power-law and exponential rates of convergence in the Birkhoff individual ergodic theorem with the same asymptotics of the probability of large deviations in this theorem.
Keywords: pointwise ergodic theorem, rates of convergence in ergodic theorems, large deviations, Anosov systems.
Mots-clés : billiards 
@article{MZM_2013_94_4_a6,
     author = {A. G. Kachurovskii and I. V. Podvigin},
     title = {Large {Deviations} and the {Rate} of {Convergence} in the {Birkhoff} {Ergodic} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {569--577},
     publisher = {mathdoc},
     volume = {94},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a6/}
}
TY  - JOUR
AU  - A. G. Kachurovskii
AU  - I. V. Podvigin
TI  - Large Deviations and the Rate of Convergence in the Birkhoff Ergodic Theorem
JO  - Matematičeskie zametki
PY  - 2013
SP  - 569
EP  - 577
VL  - 94
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a6/
LA  - ru
ID  - MZM_2013_94_4_a6
ER  - 
%0 Journal Article
%A A. G. Kachurovskii
%A I. V. Podvigin
%T Large Deviations and the Rate of Convergence in the Birkhoff Ergodic Theorem
%J Matematičeskie zametki
%D 2013
%P 569-577
%V 94
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a6/
%G ru
%F MZM_2013_94_4_a6
A. G. Kachurovskii; I. V. Podvigin. Large Deviations and the Rate of Convergence in the Birkhoff Ergodic Theorem. Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 569-577. http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a6/