A note on the Bramson-Kalikow process


We consider discrete-time stationary processes $X_n\in \{\pm 1\}$, ${n\in \Z}$, specified by a regular attractive $g$-function, similar to those considered by Bramson and Kalikow. 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.

Keywords: g-function, stationary process, memory, long-range dependence, concentration inequality.

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