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On two-block-factor sequences and one-dependence. (English) Zbl 0843.60036
Summary: 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 J. Aaronson, D. Gilat and M. Keane [J. Theor. Probab. 5, No. 3, 545-561 (1992; Zbl 0754.60070)] is not a two-block-factor.
Reviewer: Reviewer (Berlin)

##### MSC:
 60G10 Stationary stochastic processes 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60E15 Inequalities; stochastic orderings
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##### References:
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