Exchangeable measures for subshifts

J. Aaronson, H. Nakada, O. Sarig

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let Ω be a Borel subset of SN where S is countable. A measure is called exchangeable on Ω, if it is supported on Ω and is invariant under every Borel automorphism of Ω which permutes at most finitely many coordinates. De-Finetti's theorem characterizes these measures when Ω = SN. We apply the ergodic theory of equivalence relations to study the case Ω ≠ SN, and obtain versions of this theorem when Ω is a countable state Markov shift, and when Ω is the collection of beta expansions of real numbers in [0, 1] (a non-Markovian constraint).

Original languageEnglish
Pages (from-to)727-751
Number of pages25
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume42
Issue number6
DOIs
Publication statusPublished - 2006 Nov 1

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Keywords

  • Beta expansions
  • Countable Markov shifts
  • Exchangeability
  • Tail equivalence relations

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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