1660
2008
deu
preprint
1
20080430


Complete monotone coupling for Markov processes
We formalize and analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuoustime, taking values in a finite partially ordered set. Similarly to what happens in discretetime, 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 discretetime.
urn:nbn:de:kobv:517opus18286
1828
SI 990

Keine Nutzungslizenz vergeben  es gilt das deutsche Urheberrecht
Paolo Dai Pra
PierreYves 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.unipotsdam.de/files/1660/Preprint_2008_01.pdf
4872
2004
eng
preprint
0
20110329


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 DobrushinVasershtein ergodicity condition. For some special PCA, the ‘exponential ergodicity’ holds as soon as there is no phase transition.
urn:nbn:de:kobv:517opus51560
5156
SI 990

Keine Nutzungslizenz vergeben  es gilt das deutsche Urheberrecht
PierreYves 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.unipotsdam.de/files/4872/Preprint_2004_02.pdf
4873
2004
eng
preprint
0
20110329


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 SZd (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:517opus51578
5157
SI 990

Keine Nutzungslizenz vergeben  es gilt das deutsche Urheberrecht
PierreYves 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.unipotsdam.de/files/4873/Preprint_2004_04.pdf
4896
2009
eng
preprint
0
20110331


TimetoCoalescence 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 discretetime 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 timetocoalescence arising in the couplingfromthepast algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the timetocoalescence for these spatially extended models is studied too.
urn:nbn:de:kobv:517opus49454
4945
SI 990
Keine Nutzungslizenz vergeben  es gilt das deutsche Urheberrecht
PierreYves Louis
JeanBaptiste Rouquier
Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint
2009, 03
Mathematik
open_access
Institut für Mathematik
Universität Potsdam
https://publishup.unipotsdam.de/files/4896/Preprint_2009_03.pdf