TY  - JOUR
A1  - Dai Pra, Paolo
A1  - Louis, Pierre-Yves
A1  - Minelli, Ida
T1  - Monotonicity and complete monotonicity for continuous-time Markov chains
N2  - We 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 continuous time but not in discrete-time
Y1  - 2006
UR  - http://www.elsevier.com/locate/issn/1631073X
U6  - https://doi.org/10.1016/j.crma.2006.04.007
SN  - 1631-073X
ER  - 
TY  - JOUR
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 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.
Y1  - 2005
UR  - http://www.sciencedirect.com/ science?_ob=JournalURL&_cdi=5672&_auth=y&_acct=C000053886&_version=1&_urlVersion=0&_userid=1584062&md5=a190494148436adc6a 89f14409e6e76e
ER  - 
TY  - JOUR
A1  - Louis, Pierre-Yves
T1  - Ergodicity of PCA: equivalence between spatial and temporal mixing conditions
N2  - For a general attractive Probabilistic Cellular Automata on SZd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics exponentially fast in the uniform norm is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {;1, +1}Zd, with a naturally associated Gibbsian potential ;, we prove that a (spatial-) weak mixing condition (WM) for ; implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to ; holds. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
Y1  - 2004
UR  - http://www.math.washington.edu/%7Eejpecp/ECP/viewarticle.php?id=1704&layout=abstract
ER  - 
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  -