TY - JOUR

T1 - Large Deviations of the Ergodic Averages

T2 - From Hölder Continuity to Continuity Almost Everywhere

AU - Kachurovskiĭ, A. G.

AU - Podvigin, I. V.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Birkhoff’s ergodic theorem

KW - large deviations

KW - Pomeau–Manneville mapping

KW - rates of convergence in ergodic theorems

KW - return time

UR - http://www.scopus.com/inward/record.url?scp=85043507663&partnerID=8YFLogxK

U2 - 10.3103/S1055134418010029

DO - 10.3103/S1055134418010029

M3 - Article

AN - SCOPUS:85043507663

VL - 28

SP - 23

EP - 38

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -