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October, 1986 A Finite Form of De Finetti's Theorem for Stationary Markov Exchangeability
Arif Zaman
Ann. Probab. 14(4): 1418-1427 (October, 1986). DOI: 10.1214/aop/1176992383


De Finetti's theorem for stationary Markov exchangeability states that a sequence having a stationary and Markov exchangeable distribution is a mixture of Markov chains. A finite version of this theorem is given by considering a finite sequence $X_1,\ldots, X_n$ which is stationary and Markov exchangeable. It is shown that any portion of $k$ consecutive elements, say $X_1,\cdots, X_k$ for $k < n$, is nearly a mixture of Markov chains (the distance measured in the variation norm).


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Arif Zaman. "A Finite Form of De Finetti's Theorem for Stationary Markov Exchangeability." Ann. Probab. 14 (4) 1418 - 1427, October, 1986.


Published: October, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0608.60032
MathSciNet: MR866363
Digital Object Identifier: 10.1214/aop/1176992383

Primary: 60J05
Secondary: 60G10

Keywords: De Finetti's theorem , Markov chains , Markov exchangeability , Stationary processes

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 4 • October, 1986
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