Increasing coupling of probabilistic cellular automata

P.-Y. Louis

Statistics & Probability Letters, 2005, vol. 74, issue 1, 1-13

Abstract: We give a necessary and sufficient condition for the existence of an increasing coupling of N (N[greater-or-equal, slanted]2) synchronous dynamics on (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.

Keywords: Probabilistic; cellular; automata; Stochastic; ordering; Monotone; coupling (search for similar items in EconPapers)
Date: 2005
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