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.
Author details: | Pierre-Yves Louis |
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URN: | urn:nbn:de:kobv:517-opus-51578 |
Publication series (Volume number): | Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2004, 04) |
Publication type: | Preprint |
Language: | English |
Publication year: | 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 |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
License (German): | Keine öffentliche Lizenz: Unter Urheberrechtsschutz |