Exchangeable measures for subshifts

J. Aaronson; H. Nakada; O. Sarig

doi:10.1016/j.anihpb.2005.10.002

Exchangeable measures for subshifts

J. Aaronson, H. Nakada, O. Sarig

Department of Mathematics

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

Let Ω be a Borel subset of S^N 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 = S^N. We apply the ergodic theory of equivalence relations to study the case Ω ≠ S^N, 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 language	English
Pages (from-to)	727-751
Number of pages	25
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	42
Issue number	6
DOIs	https://doi.org/10.1016/j.anihpb.2005.10.002
Publication status	Published - 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

Cite this

Aaronson, J., Nakada, H., & Sarig, O. (2006). Exchangeable measures for subshifts. Annales de l'institut Henri Poincare (B) Probability and Statistics, 42(6), 727-751. https://doi.org/10.1016/j.anihpb.2005.10.002

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10.1016/j.anihpb.2005.10.002