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.
| Verfasserangaben: | Pierre-Yves Louis |
|---|---|
| URN: | urn:nbn:de:kobv:517-opus-6593 |
| Publikationstyp: | Postprint |
| Sprache: | Englisch |
| Erscheinungsjahr: | 2005 |
| Veröffentlichende Institution: | Universität Potsdam |
| Datum der Freischaltung: | 20.03.2006 |
| Freies Schlagwort / Tag: | Kopplung; stochastische Anordnung; stochastische Zellulare Automaten Probabilistic Cellular Automata; monotone coupling; stochastic ordering |
| GND-Schlagwort: | Wahrscheinlichkeitstheorie |
| Quelle: | Statistics & probability letters. - ISSN 0167-7152. - 74 (2005), 1, S. 1 - 13 |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Externe Anmerkung: | 2000 MSC: 60K35 , 60E15 , 60J10, 82C20 , 37B15 , 68W10 first published at: Statistics & Probability Letters, Volume 74, Issue 1 , 1 August 2005, Pages 1-13 |
