Research output: Contribution to journal › Article › peer-review
Large Deviations of the Ergodic Averages : From Hölder Continuity to Continuity Almost Everywhere. / Kachurovskiĭ, A. G.; Podvigin, I. V.
In: Siberian Advances in Mathematics, Vol. 28, No. 1, 01.01.2018, p. 23-38.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 10417716