TY  - GEN
A1  - Louis, Pierre-Yves
T1  - Increasing coupling for probabilistic cellular automata
N2  - 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.
KW  - Wahrscheinlichkeitstheorie
KW  - stochastische Anordnung
KW  - stochastische Zellulare Automaten
KW  - Kopplung
KW  - stochastic ordering
KW  - Probabilistic Cellular Automata
KW  - monotone coupling
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6593
ER  - 
TY  - INPR
A1  - Pra, Paolo Dai
A1  - Louis, Pierre-Yves
A1  - Minelli, Ida G.
T1  - Complete monotone coupling for Markov processes
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 01 
KW  - Markov processes
KW  - coupling
KW  - partial ordering
KW  - monotonicity conditions
KW  - monotone random
KW  - dynamical system representation
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-18286
ER  -