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 › peer-review

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

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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title = "Exchangeable measures for subshifts",

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).",

keywords = "Beta expansions, Countable Markov shifts, Exchangeability, Tail equivalence relations",

author = "J. Aaronson and H. Nakada and O. Sarig",

note = "Funding Information: * Corresponding author. E-mail addresses: aaro@tau.ac.il (J. Aaronson), nakada@math.keio.ac.jp (H. Nakada), sarig@math.psu.edu (O. Sarig). 1 Tel.: +972 3 6408805; fax: +972 3 6409357. 2 Tel.: +81 45 566 1641; fax: +81 45 566 1642. 3 The third author acknowledges support of NSF grant DMS-0500630. Tel.: +1 814 8639678; fax: +1 814 8653735.",

year = "2006",

month = nov,

doi = "10.1016/j.anihpb.2005.10.002",

language = "English",

volume = "42",

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journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

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TY - JOUR

T1 - Exchangeable measures for subshifts

AU - Aaronson, J.

AU - Nakada, H.

AU - Sarig, O.

N1 - Funding Information: * Corresponding author. E-mail addresses: aaro@tau.ac.il (J. Aaronson), nakada@math.keio.ac.jp (H. Nakada), sarig@math.psu.edu (O. Sarig). 1 Tel.: +972 3 6408805; fax: +972 3 6409357. 2 Tel.: +81 45 566 1641; fax: +81 45 566 1642. 3 The third author acknowledges support of NSF grant DMS-0500630. Tel.: +1 814 8639678; fax: +1 814 8653735.

PY - 2006/11

Y1 - 2006/11

N2 - 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).

AB - 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).

KW - Beta expansions

KW - Countable Markov shifts

KW - Exchangeability

KW - Tail equivalence relations

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

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