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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On two--block--factor sequences
and one--dependence


Author: F. Matús
Journal: Proc. Amer. Math. Soc. 124 (1996), 1237-1242
MSC (1991): Primary 60G10; Secondary 60J10, 60E15
MathSciNet review: 1301518
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Abstract: The distributions of two--block--factors $(f (\eta_{i},\eta_{i+1}); \, i \geq 1)$ arising from i.i.d. sequences $(\eta_{i}; \, i \geq 1)$ are observed to coincide with the distributions of the superdiagonals $(\zeta_{i,i+1}; \, i \geq 1)$ of jointly exchangeable and dissociated arrays $(\zeta_{i,j}; \, i, j \geq 1)$. An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.


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Additional Information

F. Matús
Affiliation: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, 182 08 Prague, Czech Republic
Email: matus@utia.cas.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03094-8
PII: S 0002-9939(96)03094-8
Keywords: $m$--dependence, block--factors, stationary sequences, partially exchangeable arrays, Markov chains, weak topology, superdiagonal
Received by editor(s): February 24, 1994
Communicated by: Richard T. Durrett
Article copyright: © Copyright 1996 American Mathematical Society