Ergodicity and central limit theorems for a class of Markov processes

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We consider a class of discrete parameter Markov processes on a complete separable metric space S arising from successive compositions of i.i.d. random maps on S into itself, the compositions becoming contractions eventually. A sufficient condition for ergodicity is found, extending a result of Dubins and Freedman [8] for compact S. By identifying a broad subset of the range of the generator, a functional central limit theorem is proved for arbitrary Lipschitzian functions on S, without requiring any mixing type condition or irreducibility.

Original languageEnglish (US)
Pages (from-to)80-90
Number of pages11
JournalJournal of Multivariate Analysis
Volume27
Issue number1
DOIs
StatePublished - Oct 1988

    Fingerprint

Keywords

  • contractions
  • functional central limit theorem
  • invariant distribution

ASJC Scopus subject areas

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

Cite this