Refine
Has Fulltext
- yes (2) (remove)
Is part of the Bibliography
- yes (2) (remove)
Keywords
- Kopplung (1)
- Markov processes (1)
- Probabilistic Cellular Automata (1)
- Wahrscheinlichkeitstheorie (1)
- coupling (1)
- dynamical system representation (1)
- monotone coupling (1)
- monotone random (1)
- monotonicity conditions (1)
- partial ordering (1)
Institute
- Institut für Mathematik (2)
- Extern (1)
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.
We formalize and analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuoustime but not in discrete-time.