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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U2 - 10.1016/j.anihpb.2005.10.002
DO - 10.1016/j.anihpb.2005.10.002
M3 - Article
AN - SCOPUS:33750194099
VL - 42
SP - 727
EP - 751
JO - Annales de l'institut Henri Poincare (B) Probability and Statistics
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
SN - 0246-0203
IS - 6
ER -