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 Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht 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 670 2006 eng postprint 0 2006-07-05 -- -- 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. Nous étudions les notions de monotonie et de monotonie complète pour les processus de Markov (ou chaînes de Markov à temps continu) prenant leurs valeurs dans un espace partiellement ordonné. Ces deux notions ne sont pas équivalentes, comme c'est le cas lorsque le temps est discret. Cependant, nous établissons que pour certains ensembles partiellement ordonnés, l'équivalence a lieu en temps continu bien que n'étant pas vraie en temps discret. urn:nbn:de:kobv:517-opus-7665 766 Comptes Rendus Mathematique. - ISSN 1631-073X. - 342 (2006), 12, S. 965 - 970 <hr>Article in English with a detailed French summary<br>First published at <a href="http://dx.doi.org/10.1016/j.crma.2006.04.007" target=_blanc>Comptes Rendus de l'Académie des Sciences de Paris - MathématiqueVolume 342, Issue 12 , 15 June 2006, Pages 965-970</a> louis@math.uni-potsdam.de Tel 1276 Paolo Dai Pra Pierre-Yves Louis Ida Minelli deu swd Stochastik eng uncontrolled continuous time Markov Chains eng uncontrolled poset eng uncontrolled monotonicity eng uncontrolled coupling Mathematik open_access Institut für Mathematik Universität Potsdam https://publishup.uni-potsdam.de/files/670/submission_CRAS_DaiPraLouisMinelli.pdf 4896 2009 eng preprint 0 2011-03-31 -- -- Time-to-Coalescence for interacting particle systems : parallel versus sequential updating Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too. urn:nbn:de:kobv:517-opus-49454 4945 SI 990 Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht Pierre-Yves Louis Jean-Baptiste Rouquier Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint 2009, 03 Mathematik open_access Institut für Mathematik Universität Potsdam https://publishup.uni-potsdam.de/files/4896/Preprint_2009_03.pdf 4872 2004 eng preprint 0 2011-03-29 -- -- Coupling, space and time Mixing for parallel stochastic dynamics We first introduce some coupling of a finite number of Probabilistic Cellular Automata dynamics (PCA), preserving the stochastic ordering. Using this tool, for a general attractive probabilistic cellular automata on SZd, where S is finite, we prove that a condition (A) is equivalent to the (time-) convergence towards equilibrium of this Markovian parallel dynamics, in the uniform norm, exponentially fast. This condition (A) means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite ‘box’-volume. For a class of reversible PCA dynamics on {−1, +1}Zd , with a naturally associated Gibbsian potential ϕ, we prove that a Weak Mixing condition for ϕ implies the validity of the assumption (A); thus the ‘exponential ergodicity’ of the dynamics towards the unique Gibbs measure associated to ϕ holds. On some particular examples of this PCA class, we verify that our assumption (A) is weaker than the Dobrushin-Vasershtein ergodicity condition. For some special PCA, the ‘exponential ergodicity’ holds as soon as there is no phase transition. urn:nbn:de:kobv:517-opus-51560 5156 SI 990 - Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht Pierre-Yves Louis Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint 2004, 02 eng uncontrolled Probabilistic Cellular Automata eng uncontrolled Interacting Particle Systems eng uncontrolled Coupling eng uncontrolled Attractive Dynamics eng uncontrolled Stochastic Ordering eng uncontrolled Weak Mixing Condition Mathematik open_access Institut für Mathematik Universität Potsdam https://publishup.uni-potsdam.de/files/4872/Preprint_2004_02.pdf 4873 2004 eng preprint 0 2011-03-29 -- -- Increasing Coupling of 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-51578 5157 SI 990 - Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht Pierre-Yves Louis Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint 2004, 04 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/4873/Preprint_2004_04.pdf 599 2004 eng postprint 0 2006-03-20 -- -- Ergodicity of PCA For a general attractive Probabilistic Cellular Automata on S-Zd, 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), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition. equivalence between spatial and temporal mixing conditions urn:nbn:de:kobv:517-opus-6589 658 ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X . - 9 (2004), S. 119 - 131 <hr>AMS 2000 Subject classification: 60G60 , 60J10 , 60K35 , 82C20 , 82C26 , 37B15<br><br>first published at:<br><a href="http://www.math.washington.edu/~ejpecp/EcpVol9/paper13.abs.html" target="_blank" >Electronic Communications in Probability, 9 (2004) paper 13, pages 119-131</a> louis@math.uni-potsdam.de + 03319771276 Pierre-Yves Louis deu swd Wahrscheinlichkeitstheorie deu uncontrolled Wechselwirkende Teilchensysteme deu uncontrolled Stochastische Zellulare Automaten eng uncontrolled Interacting particle systems eng uncontrolled Probabilistic Cellular Automata eng uncontrolled ERgodicity of Markov Chains eng uncontrolled Gibbs measures Mathematik open_access Institut für Mathematik Universität Potsdam https://publishup.uni-potsdam.de/files/599/louis01.pdf 600 2005 eng postprint 1 2006-03-20 -- -- 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 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