Increasing coupling of probabilistic cellular automata

Statistics and Probability Letters

Volumn 74, Issue 1, 2005, Pages 1-13

  Louis, P Y ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Monotone coupling; Probabilistic cellular automata; Stochastic ordering

Indexed keywords

EID: 22144444146     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2005.04.021     Document Type: Article

References (14)

1. P. Dai Pra P.-Y. Louis S. Rœlly Stationary measures and phase transition for a class of probabilistic cellular automata ESAIM Probab. Statist. 6 2002 89-104
2. D.A. Dawson Synchronous and asynchronous reversible Markov systems Canad. Math. Bull. 17 5 1974 633-649
3. J.A. Fill M. Machida Stochastic monotonicity and realizable monotonicity Ann. Probab. 29 2 2001 938-978
4. T. Kamae U. Krengel G. O'Brien Stochastic inequalities on partially ordered spaces Ann. Probab. 5 6 1977 899-912
5. T. Lindvall Lectures on the Coupling Method. Wiley Series in Probability and Mathematical Statistics Probability and Mathematical Statistics 1992 Wiley New York
6. F.J. López G. Sanz Stochastic comparisons for general probabilistic cellular automata Statist. Probab. Lett. 46 4 2000 401-410
7. Louis, P.-Y., 2002. Automates cellulaires probabilistes: Mesures stationnaires, mesures de gibbs associées et ergodicité. Ph.D. Thesis, Université de Lille 1 and Politecnico di Milano. http://tel.ccsd.cnrs.fr/documents/archives0/00/00/22/45/index_fr.html.
8. P.-Y. Louis Ergodicity of PCA: Equivalence between spatial and temporal mixing conditions Elec. Comm. Probab. 9 2004 119-131
9. C. Maes Coupling interacting particle systems Rev. Math. Phys. 5 3 1993 457-475
10. H. Thorisson Coupling, Stationarity, and Regeneration 2000 Springer New York
11. Toom, A., Vasilyev, N., Stavskaya, O., Mityushin, L., Kurdyumov, G., Pirogov, S., 1978. Locally Interacting Systems and their Application in Biology. Lecture Notes in Mathematics, vol. 653. Springer, Berlin. See also Stochastic Cellular Systems: Ergodicity, Memory, Morphogenesis, 1990, Manchester University Press.
12. See also Stochastic Cellular System: Ergodicity, Memory, Morphogenesis, 1990, Machester University Press
13. L.N. Vasershtein Markov processes over denumerable products of spaces describing large system of automata Problemy Peredačhi Informatsii 5 3 1969 64-72
14. Younes, L., 1998. Synchronous random fields and image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 20 (4).