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Increasing coupling of probabilistic cellular automata

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  • Louis, P.-Y.

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.

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  • Louis, P.-Y., 2005. "Increasing coupling of probabilistic cellular automata," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 1-13, August.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:1:p:1-13
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    References listed on IDEAS

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    1. López, F. Javier & Sanz, Gerardo, 2000. "Stochastic comparisons for general probabilistic cellular automata," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 401-410, February.
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    Cited by:

    1. Dai Pra, Paolo & Louis, Pierre-Yves & Minelli, Ida Germana, 2010. "Realizable monotonicity for continuous-time Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 959-982, June.

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