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Increasing coupling for 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
Document Type:Postprint
Year of Completion:2005
Publishing Institution:Universität Potsdam
Release Date:2006/03/20
Tag:Kopplung; stochastische Anordnung; stochastische Zellulare Automaten
Probabilistic Cellular Automata; monotone coupling; stochastic ordering
GND Keyword:Wahrscheinlichkeitstheorie
Source:Statistics & probability letters. - ISSN 0167-7152. - 74 (2005), 1, S. 1 - 13
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Notes extern:
2000 MSC: 60K35 , 60E15 , 60J10, 82C20 , 37B15 , 68W10

first published at:
Statistics & Probability Letters, Volume 74, Issue 1 , 1 August 2005, Pages 1-13