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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 greater as 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
URL:http://www.sciencedirect.com/ science?_ob=JournalURL&_cdi=5672&_auth=y&_acct=C000053886&_version=1&_urlVersion=0&_userid=1584062&md5=a190494148436adc6a 89f14409e6e76e
Document Type:Article
Year of first Publication:2005
Year of Completion:2005
Release Date:2017/03/24
Source:Statistics and Probability Letters. - 74 (2005), 1, S. 1 - 13
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert