Ergodicity and central limit theorems for a class of Markov processes

Rabi N. Bhattacharya, Oesook Lee

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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
Pages (from-to)80-90
Number of pages11
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Oct 1988

Bibliographical note

Funding Information:
supported by NSF Grant DMS 8503358.


  • contractions
  • functional central limit theorem
  • invariant distribution


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