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Increasing Coupling of Probabilistic Cellular Automata

  • We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (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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Author:Pierre-Yves Louis
Series (Serial Number):Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2004, 04)
Document Type:Preprint
Year of Completion:2004
Publishing Institution:Universität Potsdam
Release Date:2011/03/29
Tag:Probabilistic Cellular Automata; monotone coupling; stochastic ordering
RVK - Regensburg Classification:SI 990
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht