Variance bounding markov chains, L2-Uniform mean ergodicity and the clt

Yves Derriennic, Michael Lin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We prove that variance bounding Markov chains, as defined by Roberts and Rosenthal [31], are uniformly mean ergodic in L2 of the invariant probability. For such chains, without any additional mixing, reversibility, or Harris recurrence assumptions, the central limit theorem and the invariance principle hold for every centered additive functional with finite variance. We also show that L2-geometric ergodicity is equivalent to L 2-uniform geometric ergodicity. We then specialize the results to random walks on compact Abelian groups, and construct a probability on the unit circle such that the random walk it generates is L2-uniformly geometrically ergodic, but is not Harris recurrent.

Original languageEnglish
Pages (from-to)81-94
Number of pages14
JournalStochastics and Dynamics
Issue number1
StatePublished - 1 Mar 2011


  • Markov chains
  • central limit theorem
  • uniform mean ergodicity
  • variance bounding

ASJC Scopus subject areas

  • Modeling and Simulation


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