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.
| Author details: | 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 |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2005 |
| Publication year: | 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 |
