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A note on the Bramson-Kalikow process. (English) Zbl 1321.60071

Summary: We consider discrete-time stationary processes with long-range dependencies, \(X_{n}\in\{\pm1\}\), \({n\in\mathbb{Z}}\), specified by a regular attractive \(g\)-function, similar to those considered by M. Bramson and S. Kalikow [Isr. J. Math. 84, No. 1–2, 153–160 (1993; Zbl 0786.60043)]. We give an explicit set of conditions that imply the existence of at least two distinct processes specified by the same \(g\)-function, and consider a few examples that emphasize the role played by the smoothness of the majority rule at the origin.

MSC:

60G10 Stationary stochastic processes

Citations:

Zbl 0786.60043
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References:

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