TY - JOUR
T1 - Exchangeable measures for subshifts
AU - Aaronson, J.
AU - Nakada, H.
AU - Sarig, O.
N1 - Funding Information:
Acknowledgements. This work has been supported by the Integrated Graduate Program on Human-Centric Communication at Technische Universität Berlin and the German Federal Ministry of Education and Research (grant 01GQ0850).
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
UR - http://www.scopus.com/inward/record.url?scp=33750194099&partnerID=8YFLogxK
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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
SN - 0246-0203
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
IS - 6
ER -