The central limit theorem for Markov chains with normal transition operators, started at a point

Yves Derriennic, Michael Lin

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point, almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains whose transition operator is normal.

Original languageEnglish
Pages (from-to)508-528
Number of pages21
JournalProbability Theory and Related Fields
Volume119
Issue number4
DOIs
StatePublished - 1 Jan 2001

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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