The central limit theorem for Markov chains started at a point

Yves Derriennic, Michael Lin

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

The aim of this paper is to prove a central limit theorem and an invariance principle for an additive functional of an ergodic Markov chain on a general state space, with respect to the law of the chain started at a point. No irreducibility assumption nor mixing conditions are imposed; the only assumption bears on the growth of the L2-norms of the ergodic sums for the function generating the additive functional, which must be 0 (nα) with α < 1/2. The result holds almost surely with respect to the invariant probability of the chain.

Original languageEnglish
Pages (from-to)73-76
Number of pages4
JournalProbability Theory and Related Fields
Volume125
Issue number1
DOIs
StatePublished - 1 Jan 2003

ASJC Scopus subject areas

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

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