Geodesic
Large deviations of the ergodic averages: from H\"older continuity to continuity almost everywhere
Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 97-120

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

For many dynamical systems that are popular in applications, estimates are known for the decay of large deviations of the ergodic averages in the case of Hölder continuous averaging functions. In the present article, we show that these estimates are valid with the same asymptotics in the case of bounded almost everywhere continuous functions. Using this fact, we obtain, in the case of such functions, estimates for the rate of convergence in Birkhoff's ergodic theorem and for the distribution of the time of return to a subset of the phase space. 
@article{MT_2017_20_1_a5,
     author = {A. G. Kachurovskiǐ and I. V. Podvigin},
     title = {Large deviations of the ergodic averages: from {H\"older} continuity to continuity almost everywhere},
     journal = {Matemati\v{c}eskie trudy},
     pages = {97--120},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2017_20_1_a5/}
}
TY  - JOUR
AU  - A. G. Kachurovskiǐ
AU  - I. V. Podvigin
TI  - Large deviations of the ergodic averages: from H\"older continuity to continuity almost everywhere
JO  - Matematičeskie trudy
PY  - 2017
SP  - 97
EP  - 120
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2017_20_1_a5/
LA  - ru
ID  - MT_2017_20_1_a5
ER  - 
%0 Journal Article
%A A. G. Kachurovskiǐ
%A I. V. Podvigin
%T Large deviations of the ergodic averages: from H\"older continuity to continuity almost everywhere
%J Matematičeskie trudy
%D 2017
%P 97-120
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2017_20_1_a5/
%G ru
%F MT_2017_20_1_a5
A. G. Kachurovskiǐ; I. V. Podvigin. Large deviations of the ergodic averages: from H\"older continuity to continuity almost everywhere. Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 97-120. http://geodesic.mathdoc.fr/item/MT_2017_20_1_a5/