Pointwise ergodic theorems with rate and application to the CLT for Markov chains

Christophe Cuny, Michael Lin

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Let T be Dunford-Schwartz operator on a probability space (ω, μ). For f ε Lp(μ),p >1, we obtain growth conditions on || ∑ k n =1 T kf ||p which imply that 1/n 1/p ∑kn=1 T kf →0 μ-a.e. In the particular case that p = 2 and T is the isometry induced by a probability preserving transformation we get better results than in the general case; these are used to obtain a quenched central limit theorem for additive functionals of stationary ergodic Markov chains, which improves those of Derriennic-Lin and Wu-Woodroofe.

Original languageEnglish
Pages (from-to)710-733
Number of pages24
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume45
Issue number3
DOIs
StatePublished - 1 Aug 2009

Keywords

  • Central limit theorem for Markov chains
  • Dunford-Schwartz operators
  • Ergodic theorems with rates
  • Probability preserving Transformations

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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