Random walks generated by affine mappings

Marc A. Berger, H. Mete Soner

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This article is concerned with Markov chains on ℝm constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.

Original languageEnglish (US)
Pages (from-to)239-254
Number of pages16
JournalJournal of Theoretical Probability
Issue number3
StatePublished - Jul 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


  • Ergodic
  • Markov chain
  • random affine map


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