11983
2006
2006
eng
article
1
--
--
--
Monotonicity and complete monotonicity for continuous-time Markov chains
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
http://www.elsevier.com/locate/issn/1631073X
10.1016/j.crma.2006.04.007
1631-073X
allegro:1991-2014
10101158
Comptes Rendus Mathematique. - ISSN 1631-073X. - 342 (2006), 12, S. 965 - 970
Paolo Dai Pra
Pierre-Yves Louis
Ida Minelli
Institut für Mathematik
13248
2005
2005
eng
article
1
--
--
--
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.
http://www.sciencedirect.com/ science?_ob=JournalURL&_cdi=5672&_auth=y&_acct=C000053886&_version=1&_urlVersion=0&_userid=1584062&md5=a190494148436adc6a 89f14409e6e76e
allegro:1991-2014
10100710
Statistics and Probability Letters. - 74 (2005), 1, S. 1 - 13
Pierre-Yves Louis
Institut für Mathematik
Referiert
14968
2004
2004
eng
article
1
--
--
--
Ergodicity of PCA: equivalence between spatial and temporal mixing conditions
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.
http://www.math.washington.edu/%7Eejpecp/ECP/viewarticle.php?id=1704&layout=abstract
allegro:1991-2014
10100698
Electronic Communications in Probability. - 9 (2004), S. 119 - 131
Pierre-Yves Louis
Institut für Mathematik
Nicht referiert
600
2005
eng
postprint
1
2006-03-20
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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.
urn:nbn:de:kobv:517-opus-6593
659
Statistics & probability letters. - ISSN 0167-7152. - 74 (2005), 1, S. 1 - 13
<hr>2000 MSC: 60K35 , 60E15 , 60J10, 82C20 , 37B15 , 68W10<br><br>first published at:<br><a href="http://dx.doi.org/10.1016/j.spl.2005.04.021" target="_blank">Statistics & Probability Letters, Volume 74, Issue 1 , 1 August 2005, Pages 1-13 </a>
louis@math.uni-potsdam.de + 03319771276
Pierre-Yves Louis
deu
swd
Wahrscheinlichkeitstheorie
deu
uncontrolled
stochastische Anordnung
deu
uncontrolled
stochastische Zellulare Automaten
deu
uncontrolled
Kopplung
eng
uncontrolled
stochastic ordering
eng
uncontrolled
Probabilistic Cellular Automata
eng
uncontrolled
monotone coupling
Mathematik
open_access
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/files/600/louis02.pdf
1660
2008
deu
preprint
1
2008-04-30
--
--
Complete monotone coupling for Markov processes
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.
urn:nbn:de:kobv:517-opus-18286
1828
SI 990
-
Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Paolo Dai Pra
Pierre-Yves Louis
Ida G. Minelli
Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint
2008, 01
eng
uncontrolled
Markov processes
eng
uncontrolled
coupling
eng
uncontrolled
partial ordering
eng
uncontrolled
monotonicity conditions
eng
uncontrolled
monotone random
eng
uncontrolled
dynamical system representation
Mathematik
open_access
Institut für Mathematik
Extern
Universität Potsdam
https://publishup.uni-potsdam.de/files/1660/Preprint_2008_01.pdf