Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)23-38
Number of pages16
JournalSiberian Advances in Mathematics
Volume28
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Birkhoff’s ergodic theorem
  • large deviations
  • Pomeau–Manneville mapping
  • rates of convergence in ergodic theorems
  • return time

Fingerprint Dive into the research topics of 'Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere'. Together they form a unique fingerprint.

Cite this